Question

Complete the equation of the line through (3,-8)(3,−8)left parenthesis, 3, comma, minus, 8, right parenthesis and (6,-4)(6,−4

Answer 1

$y=mx+b$
$(3;-8)\rightarrow x=3;\ y=-8;\ (6;-4)\rightarrow x=6;\ y=-4$

$substitute:\\\\ \left\{\begin{array}{ccc}-8=3m+b\\-4=6m+b&|\cdot(-1)\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-8=3m+b\\4=-6m-b\end{array}\right}\ \ \ |add\ both\ sides\\.\ \ \ \ -4=-3m\ \ \ |:(-3)\\.\ \ \ \ m=\dfrac{4}{3}\\\\substitute\ the\ value\ of\ m\ to\ first\ equation:\\\\3\cdot\dfrac{4}{3}+b=-8\\\\4+b=-8\ \ \ |-4\\b=-12\\\\Answer:\boxed{y=\dfrac{4}{3}x-12}$