Geometry HELP PLEASE stuck on one question

20.
What is an equation for the line that passes through points (–1, –4) and (1, 4)? Write the equation in slope-intercept form.

Slope intercept form: y = kx + m

Where k and m are constants

Points are made up of (x, y) meaning that y is a function of x.

First lets solve k.

For two points (x1, y1) and (x2, y2) the formula for k is

k = y2-y1/x2-x1 = (with values) =(4 - (-4))/(1 - (-1)) = 8/2 = 4

so k = 4

To solve m lets use one point!

with x=1 y=4

Which means

y = kx + m yields 4 = 4*1 + m
This leads to m = 0

For sure lets test it for the last point as well

-4 = 4*(-1) + m
m=0 for that one as well

So equation in slopeform y = 4x

1) First find the slope:
y2 - y1 / x2 - x1

Therefore:
(4 - (-4)) / (1 - (-1)) = 8/2 = 4

2) Using the slope that we calculated, calculate the equation using point-slope formula:
y - y1 = m (x - x1), where m=slope

y - (-4) = 4 (x - (-1))
y + 4 = 4x + 4
y = 4x

3) Now that we found the equation, plug in the points we were provided to double-check if this works:
-4 = 4 (-1)
-4 = -4, YES

4 = 4 (1)
4 = 4, YES

Therefore, your equation for the line is y=4x.

Slope intercept form is y = mx+b where m is the slope and b is the y intercept.

Slope = rise/run = the change in y/the change in x

The 2 points given are (-1,-4) and (1,4)
the change in y is -4 to 4 = 8 units.
the change in x is -1 to 1 = 2 units
so the change in y over change in x is 8/2 which can be simplified to 4/1 (essentially written as 4).

so far we have y = 4x + b

to find the y intercept we can use the slope to make a graph or we can plug one of the given coordinates into the equation we have y = 4x + b

the y intercept is the point at which the line crosses the y axis (meaning the x value must be 0). You need to rearrange the equation to solve for b (which I earlier told you represents the y intercept).

b = mx - y

let's use the point (-1, -4) and remember the slope is 4.

b = 4(-1) - (-4)

b = (-4) - (-4)

b = -4 + 4 = 0

so your y intercept is through the origin at (0,0) making your equation y = 4x + 0 or simply y = 4x

Find slope (change in y/change in x [add in this case since I did point 2 - point 1))

m=(4+4)/(1+1)=8/2=4

Use point slope form to solve for the equation:

y+4=4(x+1)
y+4=4x+4
y=4x