Write an equation in slope-intercept form for the line that passes through the two points.
(-2, 2) and (2, -2)
To write an equation of a line in slope-intercept form (y = mx + b) that passes through two points, you'll need to find the slope (m) of the line and the y-intercept (b).
First, calculate the slope (m) using the two points (-2, 2) and (2, -2). The slope is the change in the y-coordinates divided by the change in the x-coordinates:
m = (y2 - y1) / (x2 - x1).
Using the given points (-2, 2) as (x1, y1) and (2, -2) as (x2, y2), plug the values into the formula:
m = (-2 - 2) / (2 - (-2))
m = (-4) / (4)
m = -1.
Now that you have the slope, you need to find the y-intercept (b). You can find b by taking one of the given points and plugging it into the equation with the slope:
y = mx + b.
Let's use the point (-2, 2):
2 = (-1)(-2) + b
2 = 2 + b
2 - 2 = b
b = 0.
Now that you have both m and b, you can write the equation of the line in slope-intercept form:
y = mx + b
y = -1x + 0, or, simply,
y = -x.
So the slope-intercept form of the line passing through (-2, 2) and (2, -2) is:
y = -x.