Question

A direct variation function contains the points( -8,-6) and (12,9). Which equation represents the function ?

Answer 1

Answer:

y = (3/4)x

Step-by-step explanation:

1)  Find the slope of the line.  As we go from ( -8,-6) to (12,9), x increases by 20 and y increases by 15.  Thus, the slope, m, is m = rise / run = 15/20 = 3/4

2) Recognize that the y-intercept is zero (0) because this is direct variation; the line goes thru the origin.

3) write the equation of the line:  y = mx + b becomes y = (3/4)x

Answer 2

$\bf (\stackrel{x_1}{-8}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{12}~,~\stackrel{y_2}{9}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{9-(-6)}{12-(-8)}\implies \cfrac{9+6}{12+8}\implies \cfrac{15}{20}\implies \cfrac{3}{4}$

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-6)=\cfrac{3}{4}[x-(-8)]\implies y+6=\cfrac{3}{4}(x+8) \\\\\\ y+6=\cfrac{3}{4}x+6\implies y=\cfrac{3}{4}x$