Question

A line passes through the points (2, – 2) and (3, – 9). Write its equation in slope-intercept form.

Answer 1

Explanation:

First find gradient

then use the point-slope form

y-y1 =m(x-x1)

to solve to get the slope intercept form.

y=mx+c

Answer 2

Explanation:

the easiest way to do this is (in my opinion) to start with the point-slope form, because we have 2 points of the line :

y - y1 = a(x - x1)

"a" is the slope, (x1, y1) is any point on the line (so, we can use one of the given ones).

from there we do the multiplication and simplifications to finally get the slope-intercept form

y = ax + b

"a" is again the slope, and the sum of all constant terms gives us "b", the y-intercept value (y- value when x = 0).

first, we need to get the slope. the slope is a line is the ratio

y coordinate difference / x coordinate difference

when going from one point on the line to another.

so, going from (2, -2) to (3, -9)

x changes by +1 (from 2 to 3).

y changes by -7 (from -2 to -9).

the slope is then -7/+1 = -7.

using (2, -2) as point we get

y - -2 = -7(x - 2)

y + 2 = -7x + 14

y = -7x + 12