Find an equation of the line satisfying the given conditions. write the equation using function notation. Through (-20,5) and (-36, 9) And can you show me the steps?

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Question:

find an equation of the line satisfying the given conditions. write the equation using function notation. Through (-20,5) and (-36, 9) And can you show me the steps?

Answer: The equation of the line using function notation is [tex]y=f(x)=-\frac{1}{4}x[/tex]Step-by-step explanation:Given points are (-20,5) and (-36, 9)Now to find the equation of the line passes through these pointsLet [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the two given points (-20,5) and (-36, 9) respectively.To find slope [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] [tex]m=\frac{9-5}{-36-(-20)}[/tex] [tex]m=\frac{4}{-36+20}[/tex] [tex]m=\frac{4}{-16}[/tex] [tex]m=-\frac{1}{4}[/tex]Therefore [tex]m=-\frac{1}{4}[/tex]The equation of the line is of thr form y=mx+cThe point (-20,5) passes through the above line and [tex]m=-\frac{1}{4}[/tex][tex]5=-\frac{1}{4}(-20)+c[/tex][tex]5=5+c[/tex][tex]c=0[/tex][tex]y=-\frac{1}{4}x+0[/tex]Therefore [tex]y=-\frac{1}{4}x[/tex]Therefore the equation of the line using function notation is [tex]y=f(x)=-\frac{1}{4}x[/tex]

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