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Posted on Jan 02, 2017

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Let's break this down into a few parts first.

Slope intercept form is otherwise known as y = mx + b, where m is the slope and b is the y-intercept.

Perpendicular means that the two lines will intersect each other at a 90 degree angle. In math terms, their slopes will be negative reciprocals of each other.

Starting with y + 4 = 1/4(x -7), putting into slope intercept form, y = mx + b, m = 1/4 and b=-7/4 -4.

Since it is perpendicular, it must have a slope that is a negative reciprocal. The slope of the original line is 1/4, so the multiplying it -1, we get -1/4, and taking the reciprocal, we get -4. So the slope of the perpendicular line is -4.

So, y = -4x + b, but we don't know what the value of b is. To determine this, we know the point (-4,7) is on the line that we are trying to find, so we can substitute it into the equation and calculate b to make it work.

Every time we see an x we put in -4 and every time we see a y, we put in 7.

y = -4x + b

7 = -4(-4) + b

7 = 16 + b

subtract 16 from both sides

7 - 16 = 16 + b - 16

-9 = b

Now substitute this into the equation.

y = -4x + -9

Putting it into correct form, we get y = -4x - 9.

Let's check it to see if it is correct.

It has a slope of -4, so it is perpendicular to y=1/4x - 5 3/4.

Is the point (-4,7) on the line? Let's substitute it in to see if it is on the line.

Again, everywhere we see an x, we put in -4 and everywhere we see a y we put in 7.

y= -4x - 9

7 = -4 (-4) - 9

7 = 16 - 9

7 = 7

Sorry for the very long explanation, I was being overly thorough, but after you do a few of them, you will be able to knock them off in minutes.

Good luck,

Paul

Slope intercept form is otherwise known as y = mx + b, where m is the slope and b is the y-intercept.

Perpendicular means that the two lines will intersect each other at a 90 degree angle. In math terms, their slopes will be negative reciprocals of each other.

Starting with y + 4 = 1/4(x -7), putting into slope intercept form, y = mx + b, m = 1/4 and b=-7/4 -4.

Since it is perpendicular, it must have a slope that is a negative reciprocal. The slope of the original line is 1/4, so the multiplying it -1, we get -1/4, and taking the reciprocal, we get -4. So the slope of the perpendicular line is -4.

So, y = -4x + b, but we don't know what the value of b is. To determine this, we know the point (-4,7) is on the line that we are trying to find, so we can substitute it into the equation and calculate b to make it work.

Every time we see an x we put in -4 and every time we see a y, we put in 7.

y = -4x + b

7 = -4(-4) + b

7 = 16 + b

subtract 16 from both sides

7 - 16 = 16 + b - 16

-9 = b

Now substitute this into the equation.

y = -4x + -9

Putting it into correct form, we get y = -4x - 9.

Let's check it to see if it is correct.

It has a slope of -4, so it is perpendicular to y=1/4x - 5 3/4.

Is the point (-4,7) on the line? Let's substitute it in to see if it is on the line.

Again, everywhere we see an x, we put in -4 and everywhere we see a y we put in 7.

y= -4x - 9

7 = -4 (-4) - 9

7 = 16 - 9

7 = 7

Sorry for the very long explanation, I was being overly thorough, but after you do a few of them, you will be able to knock them off in minutes.

Good luck,

Paul

Apr 03, 2016 | Office Equipment & Supplies

Slope is defined in many ways. Some use rise over run. y over x. delta y over delta x. I find the easiest way to find it is to draw a triangle to calculate the slope. I try and pick points on the line that go through the corners of the graph paper to more accurately measure the slope. The bigger the triangle the better. Now count the number of squares going up and down and the number of square going left to right. Divide the change in y by the change in x. This is your slope. If the line is going up to the right. the slope is positive. If it is going up to the left, the slope is negative.

"describe what it means in terms of the rate of change of the dependent variable per unit of the change in the independent variable."

If the y axis is distance and the x axis is time, the slope will be kilometers/hour, or speed, the rate of change.

Good luck.

Paul

"describe what it means in terms of the rate of change of the dependent variable per unit of the change in the independent variable."

If the y axis is distance and the x axis is time, the slope will be kilometers/hour, or speed, the rate of change.

Good luck.

Paul

Feb 24, 2015 | Office Equipment & Supplies

To graph (-3, -3) we start at the origin (0,0) and go 3 squares to the left and then 3 squares down.

Slope is defined in many ways, including rise/run, delta y/ delta x, etc.

Since 0 divided by anything is 0, the rise must be zero, so the slope of 0 is a horizontal line.

Put the point and the slope together, we have a horizontal line going through (-3,-3).

Good luck.

Paul

Slope is defined in many ways, including rise/run, delta y/ delta x, etc.

Since 0 divided by anything is 0, the rise must be zero, so the slope of 0 is a horizontal line.

Put the point and the slope together, we have a horizontal line going through (-3,-3).

Good luck.

Paul

Feb 04, 2015 | Office Equipment & Supplies

Simplify and put it into slope-intercept form:

y=9x-15

From the above the slope is readily seen to be 9 and the y-intercept is -15.

If this is homework be sure to show your work.

y=9x-15

From the above the slope is readily seen to be 9 and the y-intercept is -15.

If this is homework be sure to show your work.

Nov 19, 2013 | Computers & Internet

Isolate the y by subtracting 10x from both sides to get y=9-10x .

The slope is the factor of x, in this case -10 .

The intercept is the constant term, in this case 9 .

The slope is the factor of x, in this case -10 .

The intercept is the constant term, in this case 9 .

Oct 15, 2012 | Office Equipment & Supplies

That is an equation describing a straight line. The "slope-intercept" form of a line is

y = mx + b

where m is the slope (change in y-value / change in x-value)

and b is the y-intercept (the point where the line crosses the y-axis when x=0)

Positive slope means the line is rising and negative slope means it's falling.

You can rewrite the original equation 2x - 4y -9 = 0 in slope-intercept form:

y = (1/2)x - (9/4)

So you know the slope is positive 1/2 (line rises 1 y-unit for each 2 x-unit change) and crosses the y-axis at -9/4. With this information you can graph the line.

y = mx + b

where m is the slope (change in y-value / change in x-value)

and b is the y-intercept (the point where the line crosses the y-axis when x=0)

Positive slope means the line is rising and negative slope means it's falling.

You can rewrite the original equation 2x - 4y -9 = 0 in slope-intercept form:

y = (1/2)x - (9/4)

So you know the slope is positive 1/2 (line rises 1 y-unit for each 2 x-unit change) and crosses the y-axis at -9/4. With this information you can graph the line.

Jul 12, 2011 | Sewing Machines

Example: Equation of the line through (1,5) and (3,6)

Calculate the slope (gradient) of the line as a=(y2-y1)/(x2-x1) where y2=6, y1=5, x2=3, and x1=1. You should get a=(6-5)/(3-1)=1/2

The equation is y=(1/2)x PLUS b, where b is not known yet.

To find b, substitute the coordinates of one of the points in the equation. Let us do it for (3,6).

The point (3,6) lies on the line, so 6=3/2 PLUS b.

Solve for b: 6 MINUS 3/2=b, or b=9/2=4.5

Equation is thus y=(x/2) PLUS 9/2 =(x PLUS 9)/2

Calculate the slope (gradient) of the line as a=(y2-y1)/(x2-x1) where y2=6, y1=5, x2=3, and x1=1. You should get a=(6-5)/(3-1)=1/2

The equation is y=(1/2)x PLUS b, where b is not known yet.

To find b, substitute the coordinates of one of the points in the equation. Let us do it for (3,6).

The point (3,6) lies on the line, so 6=3/2 PLUS b.

Solve for b: 6 MINUS 3/2=b, or b=9/2=4.5

Equation is thus y=(x/2) PLUS 9/2 =(x PLUS 9)/2

Jan 10, 2011 | Texas Instruments TI-84 Plus Calculator

Calculate
the slope (gradient) of the line as a=(y2-y1)/(x2-x1) where y2=6, y1=5,
x2=3, and x1=1. You should get a=(6-5)/(3-1)=1/2

The equation is y=(1/2)x PLUS b, where b is not known yet.

To find b, substitute the coordinates of one of the points in the equation. Let us do it for (3,6).

The point (3,6) lies on the line, so 6=3/2 PLUS b.

Solve for b: 6 MINUS 3/2=b, or b=9/2=4.5

Equation is thus y=(x/2) PLUS 9/2 =(x PLUS 9)/2

The equation is y=(1/2)x PLUS b, where b is not known yet.

To find b, substitute the coordinates of one of the points in the equation. Let us do it for (3,6).

The point (3,6) lies on the line, so 6=3/2 PLUS b.

Solve for b: 6 MINUS 3/2=b, or b=9/2=4.5

Equation is thus y=(x/2) PLUS 9/2 =(x PLUS 9)/2

Oct 20, 2010 | Texas Instruments TI-84 Plus Calculator

It depends on how complex the function is; there are different techniques. For a straight line of the standard form, usually shown as y=mx+b; this is a simple function of y in terms of x. So, determining the function in this case means finding values for m and b. --- m is the slope of the line, commonly called rise over run. Since your question asks in terms of coordinates, I would assume that you are looking at a problem giving you 2 points.

Probably something like p1 = (3,4); p2 = (5,8); the general form of this is p1=(x1,y1); p2=(x2,y2). The slope in this case is rise over run, in other words, the change in y divided by the change in x. This can be calculate between these two points as (y2-y1)/(x2-x1). In my sample above, this would be (8-4)/(5-3) = 4/2 = 2 giving the value of m.

To find the value of b (the y intercept) you need the value of y when x = 0. Since you already know that m, the slope is 2, consider a new point, call it p3 (x3,y3), pick either of the known points and solve the slope equation again, this time for y3. [m=(y3-y1)/(x3-x1)]. We know that x3 is 0, since we are trying to solve for y where that is true, so the equation becomes:

m=(y3-y1)/(-x1)

-x1*m=y3-y1

y3=y1-x1*m

y3 is really b in the standard form, since it is, by definition the intercept, or the value when x=0,

so

b=y1-x1*m -- this gives you the y intercept anytime you know the slope and one point on the line.

In the example, y1 = 4, x1=3 and we've already calculated m to be 2, so

b=4-3*2 = -2

So, the function would be

y = 2x -2

To check, plug in the values of the other point, p2, and see if they work

y2 = 2*x2 - 2

8=2*5-2

It's easier than it looks. It can help you to understand if you get some old fashioned graph paper and plot it so you can see what is happening.

Probably something like p1 = (3,4); p2 = (5,8); the general form of this is p1=(x1,y1); p2=(x2,y2). The slope in this case is rise over run, in other words, the change in y divided by the change in x. This can be calculate between these two points as (y2-y1)/(x2-x1). In my sample above, this would be (8-4)/(5-3) = 4/2 = 2 giving the value of m.

To find the value of b (the y intercept) you need the value of y when x = 0. Since you already know that m, the slope is 2, consider a new point, call it p3 (x3,y3), pick either of the known points and solve the slope equation again, this time for y3. [m=(y3-y1)/(x3-x1)]. We know that x3 is 0, since we are trying to solve for y where that is true, so the equation becomes:

m=(y3-y1)/(-x1)

-x1*m=y3-y1

y3=y1-x1*m

y3 is really b in the standard form, since it is, by definition the intercept, or the value when x=0,

so

b=y1-x1*m -- this gives you the y intercept anytime you know the slope and one point on the line.

In the example, y1 = 4, x1=3 and we've already calculated m to be 2, so

b=4-3*2 = -2

So, the function would be

y = 2x -2

To check, plug in the values of the other point, p2, and see if they work

y2 = 2*x2 - 2

8=2*5-2

It's easier than it looks. It can help you to understand if you get some old fashioned graph paper and plot it so you can see what is happening.

Jun 16, 2009 | Computers & Internet

The slope is measured off the horizontal plane. A 45 degree slope would rise 12 inches for every 12 inches of horizontal travel in this example. If the slope is too great try checking kits made by Fanimation. The Fanimation SCK52 - 52 Degree Ceiling Slope Ceiling Fan Kit will go up to a 52 degree angle ceiling and will fit most downrods. The hampton bay fans are very popular and should work just fine with this kit.

-Mark

-Mark

May 14, 2009 | Hampton Bay 52 In. White Huntington III...

Jul 18, 2018 | The Office Equipment & Supplies

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