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.
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.
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