Question

A line passes through the points ( − 16 , 14 ) and ( 8 , 35 ) . Calculate the slope of the line - simplify answer if possible. (If the slope is undefined, enter "DNE") Then, write the equation of the line.

Answer 1

Given two points $(x_1,y_1),\ (x_2,y_2)$, the slope of the line connecting them is defined as

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

In your case, the points are

$(x_1,y_1)=(-16,14),\ (x_2,y_2)=(8,35)$

Plugging these values in the slope formula gives

$m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{35-14}{8-(-16)}=\dfrac{21}{24}=\dfrac{7}{8}$