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Find the equation of the line passing through the line (3,- 4) and (8, - 8)

Sagot :

Answer:

[tex]y=-\frac{4}{5}x-\frac{8}{5}[/tex]

First, let us find the slope of the line using the following equation:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Using the points (3, -4) and (8, -8)

[tex]m=\frac{y_2-y_1}{x_2-x_1}\Rightarrow m=\frac{-8-(-4)}{8-3}[/tex][tex]m=\frac{-8+4}{8-3}=\frac{-4}{5}\Rightarrow m=-\frac{4}{5}[/tex]

Now that we found the slope of the line, we are going to use the following equation to solve for the equation of the line:

[tex]y-y_1=m(x-x_1)[/tex]

Using the point (3, -4)

[tex]y-y_1=m(x-x_1)\Rightarrow y-(-4)=-\frac{4}{5}(x-3)[/tex][tex]y+4=-\frac{4}{5}x+\frac{12}{5}\Rightarrow y=-\frac{4}{5}x+\frac{12}{5}-4[/tex][tex]y=-\frac{4}{5}x-\frac{8}{5}[/tex]

Therefore, the equation of the line that passes through the points (3, -4) and (8, -8) is:

[tex]y=-\frac{4}{5}x-\frac{8}{5}[/tex]