the slope-intercept form of a straight line is

y = mx + b, where 'm' is the slope and 'b' gives the y-intercept

to find the slope, we use the following formula:

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

where (x1, y1) and (x2 , y2) are two points from the line

in our case we can write (x1, y1) = (12, −2) and (x2 , y2) = (18, 34) therefore the slope is

m = (-2 - 34) / (12 - 18) = -36/(-6) = 6

m = 6

now the equation is y = 6x + b. the only thing left to find is b.

we pick one of the points (it doesn't matter which one), and use it to solve for b.

using the point (12, -2), we get:

-2 = 6*12 + b

72 + b = -2

b = -74

the slope-intercept form of the equation is

y = 6x - 74