3x+y=4

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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.

Parallel means that the two lines will never meet. They are parallel to each other. In math terms, their slopes are the same, so the m values must be the same.

Starting with y = -5x + 1, putting into slope intercept form, y = mx + b, m = -5 and b=1.

Since it is parallel, it must have the same slope and the m values are the same.

So, y = -5x + b, but we don't know what the value of b is. To determine this, we know the point (-4,-6) 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 -6.

-6 = -5(-4) + b

-6 = 20 + b

subtract 20 from both sides

-6 - 20 = 20 + b - 20

-26 = b

Now substitute this into the equation.

y = -5x + -26

Putting it into correct form, we get y = -5x - 26.

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

It has a slope of -5, so it is parallel to y=-5x + 1

Is the point (-4,-6) 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 -6.

-6 = -5(-4) - 26

-6 = 20 - 26

-6 = -6

Sorry for the very long explanation, 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.

Parallel means that the two lines will never meet. They are parallel to each other. In math terms, their slopes are the same, so the m values must be the same.

Starting with y = -5x + 1, putting into slope intercept form, y = mx + b, m = -5 and b=1.

Since it is parallel, it must have the same slope and the m values are the same.

So, y = -5x + b, but we don't know what the value of b is. To determine this, we know the point (-4,-6) 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 -6.

-6 = -5(-4) + b

-6 = 20 + b

subtract 20 from both sides

-6 - 20 = 20 + b - 20

-26 = b

Now substitute this into the equation.

y = -5x + -26

Putting it into correct form, we get y = -5x - 26.

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

It has a slope of -5, so it is parallel to y=-5x + 1

Is the point (-4,-6) 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 -6.

-6 = -5(-4) - 26

-6 = 20 - 26

-6 = -6

Sorry for the very long explanation, 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

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

A great tutorial: https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/8th-slope-intercept-form/v/linear-equations-in-slope-intercept-form

Mar 17, 2015 | math.com Computers & Internet

The slope is 3 and the y-intercept is 6.

Oct 15, 2014 | Office Equipment & Supplies

Assuming the 'standard form' is "slope-intercept", calculate the slope from the equation m = __y2-y1__ =__ 5 - 1__ = __ 4__ = -2

x2-x1 4 - 6 -2

The intercept can be found by substituting either of the two points into the equation y = mx + b

5 = (-2)4 + b

5 = (-8) + b

13 = b

(OR, using the other point, y = mx + b

1 = (-2)6 + b

1 = (-12) + b

13 = b )

Then expressing in general:

**y = (-2) x + 13**

x2-x1 4 - 6 -2

The intercept can be found by substituting either of the two points into the equation y = mx + b

5 = (-2)4 + b

5 = (-8) + b

13 = b

(OR, using the other point, y = mx + b

1 = (-2)6 + b

1 = (-12) + b

13 = b )

Then expressing in general:

Oct 10, 2014 | Computers & Internet

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

That's a little difficult since there is no y in the equation.

Nov 19, 2013 | Computers & Internet

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

use the slope-intercept form to graph y=2/3x+4

Mar 31, 2010 | Computers & Internet

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