Question

what is the equation in slope intercept form of the line that passes through the point (-4,47) and (2,-16)

Answer 1

The slope-intercept form:

$y=mx+b$

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (-4, 47) and (2, -16). Substitute:

$m=\dfrac{-16-47}{2-(-4)}=\dfrac{-63}{6}=-\dfrac{63:3}{6:3}=-\dfrac{21}{2}$

Therefore we have:

$y=-\dfrac{21}{2}x+b$

Put the coordinates of the point (2, -16) to the equation:

$-16=-\dfrac{21}{2}(2)+b\\\\-16=-21+b\qquad\text{add 21 from both sides}\\\\5=b\to b=5$

Answer: $\boxed{y=-\dfrac{21}{2}x+5}$