Question

slope form for (-2,4),(2,-1)

Answer 1

To find the slope-intercept form of a linear equation given two points, you need to find the slope (m) first. The formula for finding the slope (m) is:

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

Let's plug in the values for the points (-2, 4) and (2, -1):

m = (-1 - 4) / (2 - (-2))
m = (-1 - 4) / (2 + 2)
m = (-5) / (4)
m = -5/4

Now, we have the slope (m = -5/4). The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. To find the y-intercept (b), we can use one of the given points. Let's use the point (-2, 4):

y = mx + b
4 = (-5/4)(-2) + b
4 = (10/4) + b
4 = 5/2 + b

To isolate b, we subtract 5/2 from both sides of the equation:

4 - 5/2 = b
8/2 - 5/2 = b
3/2 = b

Now, we have the y-intercept (b = 3/2). Therefore, the slope-intercept form for the given points (-2, 4) and (2, -1) is:

y = (-5/4)x + 3/2