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.

Answers

Answered by GPT 3.5
To find the equation of a line passing through two points (-2,-4) and (2,4), we can use the slope-intercept form of a linear equation, which is given by y = mx + b, where m is the slope of the line and b is the y-intercept.

Step 1: Find the slope (m) of the line.
The slope (m) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Substitute the coordinates of the two points into the formula:
m = (4 - (-4)) / (2 - (-2))
m = 8 / 4
m = 2

Step 2: Substitute the slope (m) and one of the points into the slope-intercept form (y = mx + b) to solve for b.
We can use either of the two points. Let's use the point (-2,-4).
y = mx + b
-4 = 2*(-2) + b
-4 = -4 + b
b = -4 + 4
b = 0

Step 3: Write the equation using the slope (m) and y-intercept (b).
The equation of the line is:
y = 2x + 0
Simplifying, we can write:
y = 2x

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