Question

Write the slope-intercept form of the equation of a line that passes through the points (-2,-4) and (2,4). Enter your answer below and show all the steps that you used to solve this problem for full credit. (2 points)

Answer 1

To find the slope-intercept form of the equation of a line that passes through the points (-2,-4) and (2,4), we need to find the slope and the y-intercept.

Step 1: Find the slope (m).
The formula for finding the slope (m) between two points (x1, y1) and (x2, y2) is:

m = (y2 - y1) / (x2 - x1)

Substituting the values from the given points (-2,-4) and (2,4):

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

Therefore, the slope (m) is 2.

Step 2: Find the y-intercept (b).
We can use the slope-intercept form of the equation, y = mx + b, where m is the slope and b is the y-intercept. We can substitute the values we know:

-4 = 2(-2) + b
-4 = -4 + b
b = -4 + 4
b = 0

Therefore, the y-intercept (b) is 0.

Step 3: Write the equation in slope-intercept form.
Using the values we found for the slope (m) and the y-intercept (b), we can write the equation in slope-intercept form:

y = mx + b
y = 2x + 0
y = 2x

Therefore, the slope-intercept form of the equation of the line passing through the points (-2,-4) and (2,4) is y = 2x.