Question

find an equation of the line that passes through the given point and has the indicated slope m.
question 1: (0,-2), m = 3
question 2: (-3, 6), m = -2
question 3: (4,0), m = -1/3

Answer 1

use the point-slope form
\[y-y_1 = m(x-x_1) \]
then solve for y

Answer 2

so what you want to do is plug the slope value (m) into the basic y=mx+b equation. then plug the point (x,y) into the equation and solve for b

Answer 3

an example
given a point (4, 1) and a slope of 5, find the equation of a line

solution:
first assign
\[m = 5\]
\[x_1 = 4\]
\[y_1 = 1\]
using the point-slope form
\[y - 1 = 5 (x-4) \rightarrow y-1 = 5x - 20\]
solve for y
\[y - 1 + 1 = 5x - 20 + 1 \rightarrow y = 5x -19\]