write the equation of the line passing through the points (-2,4) and (1,-5) in slope intercept form.?

slope-intercept format looks like this:

y = mx + c

where m and c are usually numbers, and where

m is the slope = how fast y rises, when x goes up by 1,

c is the y-intercept (the value of y, when x=0)

In an ordered pair, the coordinates are given in the order of (x, y)

for these points, x goes from -2 to + 1 (an increase of +3)

while y goes from 4 to -5 (a "rise" of -9 -- in other words, a decrease)

The slope is, therefore, -9/3 = -3

Every time x goes up by 1, y goes DOWN by 3.

m = -3

So far, we have

y = -3x + c

To find the value of c, we simply pick one point

say (x, y) = (-2, 4)

We use these values in the equation, and solve for c

y = -3x + c

becomes

4 = -3(-2) + c

4 = 6 + c

-2 = c

We now have everything we need. We put it all together

y = mx + c

is now

y = -3x - 2

We check this with the other point (x, y) = (1, -5)

-5 = -3(1) - 2

-5 = -3 - 2

TRUE

m = (4 - (-5))/(-2 - 1) = -3, so

y = -3x + b, where b is found from

(4) = -3(-2) + b => b = -2.

Answer: y = -3x - 2.