Question

If the slope of a line and a point on the line are​ known, the equation of the line can be found using the​ slope-intercept form, y=mx+b. To do​ so, substitute the value of the slope and the values of x and y using the coordinates of the given​ point, then determine the value of b.

Using the above​ technique, find the equation of the line containing the points ​(-8​,19​) and (4,-2)

Answer 1

Explanation:

the slope (m) of a line is the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.

so, going from (-8, 19) to (4, -2)

x changes by +12 (from -8 to 4).

y changes by -21 (from 19 to -2).

the slope (m) is therefore

-21/+12 = -7/4

and by using (4, -2) as the point, we get

-2 = -7/4 × 4 + b = -7 + b

5 = b

and the full equation is

y = (-7/4)x + 5