Write an equation in slope-intercept form for the line that passes through the two points.
(-2, 2) and (2, -2)
To write the equation of a line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept, you first need to calculate the slope of the line using the two given points.
The slope (m) of the line that passes through two points (x1, y1) and (x2, y2) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the given points (-2, 2) and (2, -2), we have:
m = (-2 - 2) / (2 - (-2))
m = (-4) / (4)
m = -1
Now we have the slope, which is -1. To get the y-intercept (b), we can use one of the points and plug it into the equation along 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
So the y-intercept is 0.
Now we can write the equation of the line in slope-intercept form:
y = mx + b
y = -1x + 0
Since the y-intercept is 0, we can simply write the equation as:
y = -1x or y = -x
This is the equation of the line in slope-intercept form that passes through the points (-2, 2) and (2, -2).