Question about Riverdeep Mighty Math Cosmic Geometry (1073) for PC, Mac

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Posted on Jan 02, 2017

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The easiest way to solve and graph and equation is to put the equation into the slope intercept form y = mx + b, where m is the slope and b in the y-intercept.

To do this, we subtract 4x from both sides and get y = -4x + 0.

From this we know m = -4 (slope) and the y-intercept is 0.

I always start with the y-intercept and put a point there. Thus, we have a point at (0,0). Using this as a starting point, we now use the slope of -4 to get future points. Since it is negative, we go one unit to the left and up four units. So we have the point (-1,4). Using a ruler, we connect these points and continue on both sides to produce the line.

There is also a great free online program/app called Desmos that you can use to check your work. Type in the equation of the line and it will graph it for you.

Good luck,

Paul

To do this, we subtract 4x from both sides and get y = -4x + 0.

From this we know m = -4 (slope) and the y-intercept is 0.

I always start with the y-intercept and put a point there. Thus, we have a point at (0,0). Using this as a starting point, we now use the slope of -4 to get future points. Since it is negative, we go one unit to the left and up four units. So we have the point (-1,4). Using a ruler, we connect these points and continue on both sides to produce the line.

There is also a great free online program/app called Desmos that you can use to check your work. Type in the equation of the line and it will graph it for you.

Good luck,

Paul

Oct 27, 2016 | Office Equipment & Supplies

The "slope intercept form of the equation of a (the) line" is y=mx+b, where m is the slope of the line and b is the y-intercept.

We are given the slope of 1/2, so m= 1/2.

We can now write y=1/2 x + b.

Since the point (-2,-3) is on the line, we can substitute it in and solve for b. We put the -2 in for x and -3 in for y.

-3 = 1/2(-2) +b

-3 = -1 + b

-3 + 1 = -1 + b +1

-2 =b

Thus, the equation of the line is y= 1/2 x -2

To check if we did this correctly, plug in the point (-2, -3) to see if it works.

Left Side Right Side

-3 = 1/2 (-2) -2

= -1-2

= -3

We are given the slope of 1/2, so m= 1/2.

We can now write y=1/2 x + b.

Since the point (-2,-3) is on the line, we can substitute it in and solve for b. We put the -2 in for x and -3 in for y.

-3 = 1/2(-2) +b

-3 = -1 + b

-3 + 1 = -1 + b +1

-2 =b

Thus, the equation of the line is y= 1/2 x -2

To check if we did this correctly, plug in the point (-2, -3) to see if it works.

Left Side Right Side

-3 = 1/2 (-2) -2

= -1-2

= -3

Feb 24, 2015 | Office Equipment & Supplies

If your equation can be written in the form of a function (y=f(x)),

the slope of the function at a point is the derivative of the function at the point. For any function that is not a constant or linear, you need calculus to find the slope.

If the function is of the form y= ax +b, the slope is the value a.

the slope of the function at a point is the derivative of the function at the point. For any function that is not a constant or linear, you need calculus to find the slope.

If the function is of the form y= ax +b, the slope is the value a.

Mar 21, 2014 | Texas Instruments TI-84 Plus Calculator

- Transform this equation to its functional form:
- 9y=-3x+17 or
**y=(-1/3)x+17/9** - In the last equation, the slope is the coefficient of x, namely
**-1/3.** - A line parallel to this one must have the same slope (-1/3).
- So the equation of your line starts this way:
**y=(-1/3)x+b.** - To identify (calculate)
**b**, you must make use of the fact that the parallel line passes through the point (1,5). - That means that the coordinates of the point (1,5) satisfy the equation of the parallel line y=(-1/3)x+b
- Substitute 5 for y, and 1 for x and solve for b.

Aug 05, 2012 | Office Equipment & Supplies

The equation of a straight line can be cast into several forms: functional form, general form, symmetrical form. The functional form is the one usually known as slope intercept form.

In the functional form, y=ax+b or sometimes y=mx+b, the factor of the x-variable (a or m as the case may be) is the slope of the straight line, and the value b, is the ordinate (y-value) of the point where the straight line cuts (intercepts) the y-axis.

Since you say nothing about the particulars of the line that interests you, there is not much more that anybody can help you with.

In the functional form, y=ax+b or sometimes y=mx+b, the factor of the x-variable (a or m as the case may be) is the slope of the straight line, and the value b, is the ordinate (y-value) of the point where the straight line cuts (intercepts) the y-axis.

Since you say nothing about the particulars of the line that interests you, there is not much more that anybody can help you with.

Mar 25, 2012 | SoftMath Algebrator - Algebra Homework...

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

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

Calculate the slope (gradient) of the line as a=(y2-y1)/(x2-x1) where y2=1, y1=0, x2=0, and x1=-6. You should get a=(1-0)/(0-(-6))=1/6

The y-intercept is the y-cordinate for x=0. Its value is 1.

The equation is then y=(x/6) 1.

The y-intercept is the y-cordinate for x=0. Its value is 1.

The equation is then y=(x/6) 1.

Oct 18, 2010 | Texas Instruments TI-84 Plus Calculator

assuming the question is what is the circle equation?

and if (-2,2) is the center of the circle

the equation should look like this: (x+2)^2+(Y-2)^2=R^2

And now only R is needed.

given 2x-5y+4=0 equation of line perpendicular

we can rearange the equation to be y=(2x+4)/5

from that we can see that the slope of the line is 2/5

And from the fact of perpendicular line we can say that the slope

of the radius line is -2/5.

The motivation now is to calculate the distance between the center of the circle to the cross point of the radius with the line perpendicular

For that we would calculate the radius line equation and compare it to the equation of line perpendicular

As mentioned earlier the slope of the radious line is -2/5.

So the equation is y=-2/5x+b and b can be calculated by using the center of the circle coordinates

2= - (2/5)*(-2)+b ------> b=2-4/5=1.2

radius equation is y=-(2/5)x+1.2

Now the cross point is calculated by comparing the equations:

-(2/5)x+1.2=(2x+4)/5 --> -2x+6=2x+4 --> 4x=2 --> x=1/2 --> y=1

So the cross point is (1/2,1).

The distance between the points is calculated by the following

Formula:

R=SQR(((1/2)-(-2))^2+(2-1)^2)=SQR(2.5^2+1^2)=SQR(6.25+1)=

SQR(7.25)

Therefore the circle eq is (x+2)^2+(Y-2)^2=7.25

and if (-2,2) is the center of the circle

the equation should look like this: (x+2)^2+(Y-2)^2=R^2

And now only R is needed.

given 2x-5y+4=0 equation of line perpendicular

we can rearange the equation to be y=(2x+4)/5

from that we can see that the slope of the line is 2/5

And from the fact of perpendicular line we can say that the slope

of the radius line is -2/5.

The motivation now is to calculate the distance between the center of the circle to the cross point of the radius with the line perpendicular

For that we would calculate the radius line equation and compare it to the equation of line perpendicular

As mentioned earlier the slope of the radious line is -2/5.

So the equation is y=-2/5x+b and b can be calculated by using the center of the circle coordinates

2= - (2/5)*(-2)+b ------> b=2-4/5=1.2

radius equation is y=-(2/5)x+1.2

Now the cross point is calculated by comparing the equations:

-(2/5)x+1.2=(2x+4)/5 --> -2x+6=2x+4 --> 4x=2 --> x=1/2 --> y=1

So the cross point is (1/2,1).

The distance between the points is calculated by the following

Formula:

R=SQR(((1/2)-(-2))^2+(2-1)^2)=SQR(2.5^2+1^2)=SQR(6.25+1)=

SQR(7.25)

Therefore the circle eq is (x+2)^2+(Y-2)^2=7.25

Oct 26, 2008 | Casio FX-115ES Scientific Calculator

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