MATH SOLVE

2 months ago

Q:
# Match each graph to the equation of its line.

Accepted Solution

A:

Answer with explanation:If the graph passes through two points (a,b) and (c,d) then the equation of line is: [tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]1)If the graph passes through (1,0) and (0,-4)Then the equation of line is: [tex]y-0=\dfrac{-4-0}{0-1}\times (x-1)\\\\\\y=\dfrac{-4}{-1}\times (x-1)\\\\\\i.e.\\\\\\y=4(x-1)\\\\\\y=4x-4[/tex]2)If the graph passes through (-2,0) and (0,2)The equation of line is: [tex]y-0=\dfrac{2-0}{0-(-2)}\times (x-(-2))\\\\\\i.e.\\\\\\\\y=\dfrac{2}{2}\times (x+2)\\\\\\i.e.\\\\\\y=x+2[/tex]3)If the graph passes through (-2,0) and (0,-4)The equation of line is: [tex]y-0=\dfrac{-4-0}{0-(-2)}\times (x-(-2))\\\\i.e.\\\\y=\dfrac{-4}{2}\times (x+2)\\\\\\i.e.\\\\\\y=-2(x+2)\\\\\\i.e.\\\\\\y=-2x-4[/tex]4)If the graph passes through (2,0) and (0,2)The equation of line is:[tex]y-0=\dfrac{2-0}{0-2}\times (x-2)\\\\\\i.e.\\\\\\y=\dfrac{-2}{2}\times (x-2)\\\\\\i.e.\\\\\\y=-(x-2)\\\\\\i.e.\\\\\\y=-x+2[/tex]