Mathematics: Match each graph to the equation of its line.

uhm chile s anywayzzStep-by-step explanation:...

Match each graph to the equation of its line.

ltay92

04.01.2022

Answer with explanation:

If the graph passes through two points (a,b) and (c,d) then the equation of line is:

$y-b=\dfrac{d-b}{c-a}\times (x-a)$

If the graph passes through (1,0) and (0,-4)

Then the equation of line is:

$y-0=\dfrac{-4-0}{0-1}\times (x-1)\\\\\\y=\dfrac{-4}{-1}\times (x-1)\\\\\\i.e.\\\\\\y=4(x-1)\\\\\\y=4x-4$

If the graph passes through (-2,0) and (0,2)

The equation of line is:

$y-0=\dfrac{2-0}{0-(-2)}\times (x-(-2))\\\\\\i.e.\\\\\\\\y=\dfrac{2}{2}\times (x+2)\\\\\\i.e.\\\\\\y=x+2$

If the graph passes through (-2,0) and (0,-4)

The equation of line is:

$y-0=\dfrac{-4-0}{0-(-2)}\times (x-(-2))\\\\i.e.\\\\y=\dfrac{-4}{2}\times (x+2)\\\\\\i.e.\\\\\\y=-2(x+2)\\\\\\i.e.\\\\\\y=-2x-4$

If the graph passes through (2,0) and (0,2)

The equation of line is:

$y-0=\dfrac{2-0}{0-2}\times (x-2)\\\\\\i.e.\\\\\\y=\dfrac{-2}{2}\times (x-2)\\\\\\i.e.\\\\\\y=-(x-2)\\\\\\i.e.\\\\\\y=-x+2$

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