Question

Write the equation of the line that passes through the points (0, -2) and (-1,0).

Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal
line.

Answer 1

Explanation:

point-slope firm is

y - y1 = m(x - x1)

m = slope of the line

(x1, y1) = coordinates of one point on the line.

the slope is the ratio y/x, which indicates how many units y is changing, when x changes a certain amount of units.

when we look at the 2 given points, we go from one point to the other - how much are x and y changing ?

let's just go in the direction of the original listing. so, we go from (0, -2) to (-1, 0).

x changes from 0 to -1, so, by -1.

y changes from -2 to 0, so, by +2

so, our slope is saying that when x changes by -1 unit, y changes 2 units.

=> m = y/x = 2/-1 = -2

so, as equation we get (by using the first point)

y - -2 = -2(x - 0) = -2x

y + 2 = -2x

or fully simplified leading to the slope-intercept form

y = -2x - 2