The general equation of a line which passes through (x0,y0) is

(y - y0) = m*(x - x0) m - is the slope of the line

slope = how many units does a close climb/descends on a specified horizontal distance

Lets consider (x0,y0) = (-2,1)

The equation of a line that passes through (-2,1) is

y-1 = m(x+2)

In order for it to pass through the second point (x1,y1)=(5,-2) we have to specify an appropriate slope.

M=(y0-y1)/(x0-x1) - see the definition above

so m is

m=(-2-1)/(5-(-2)) = -3/7

your answer is

y-1 = -3/7 * (x+2)

(y - y0) = m*(x - x0) m - is the slope of the line

slope = how many units does a close climb/descends on a specified horizontal distance

Lets consider (x0,y0) = (-2,1)

The equation of a line that passes through (-2,1) is

y-1 = m(x+2)

In order for it to pass through the second point (x1,y1)=(5,-2) we have to specify an appropriate slope.

M=(y0-y1)/(x0-x1) - see the definition above

so m is

m=(-2-1)/(5-(-2)) = -3/7

your answer is

y-1 = -3/7 * (x+2)