Answered

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Write the equation of the line that passes through the points (8, -1) and (2, -5) inpoint-slope form.

Sagot :

First, we find the slope using the given points and the formula below

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-5-(-1)}{2-8}=\frac{-5+1}{-6}=\frac{-4}{-6}=\frac{2}{3}[/tex]

Then, we use the point-slope formula to find the equation

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

Let's replace the point (8, -1) and the slope 2/3.

[tex]\begin{gathered} y-(-1)=\frac{2}{3}(x-8) \\ y+1=\frac{2}{3}x-\frac{16}{3} \\ y=\frac{2}{3}x-\frac{16}{3}-1 \\ y=\frac{2}{3}x+\frac{-16-3}{3} \\ y=\frac{2}{3}x-\frac{19}{3} \end{gathered}[/tex]

Hence, the equation in point-slope form is

[tex]y+1=\frac{2}{3}(x-8)[/tex]

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