Question

Write the equation of the line through the points (8, -7) and (-2, 8).

Answer 1

y=-3/2x+5

Explanation:

you devide a substract form y2-y1 and x2-x1 and you get a k=-3/2. than you insert the numbers(8.-7 or -2,8) into the equasion y=-3/2x+n and you find n=5

Answer 2

`\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{The\:points\:are \to \ (x_1=8,y_1=-7) \ and \ (x_2=-2,y_2=8)} \end{gathered}$}}`

We use the formula of the canonical equation of the line:

`\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{(x-x_1)/(x_2-x_1)=(y-y_1)/(y_2-y_1) } \end{gathered}$}}`

Let's put in the formula the coordinates of points:

`\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{(x-8 )/((-2)-8)=(y-(-7) )/(8-(-7)) } \end{gathered}$}}`

Canonical equation of the line:

`\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{(x-8 )/(-10)=(y+7)/(15) } \end{gathered}$}}`

From a parametric equation of the line we find the general equation of the line:

`\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{y=-1.5x+5 } \end{gathered}$}}}`