The general slope-intercept equation of a line is:
[tex]y=m\cdot(x-x_1)+y_1\text{.}[/tex]
Where:
• m is the slope of the line,
,
• (x1, y1) are the coordinates of one point of the line.
The slope of the line can be computed by the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\text{.}[/tex]
Where (x1, y1) and (x2, y2) are coordinates of two points of the line.
In this problem, we have a line that passes through the points:
• (x1, y1) = (-7, 7),
,
• (x2, y2) = (14, -2).
Replacing the data of the points in the equation of m, we get:
[tex]m=\frac{-2-7}{14-(-7)}=-\frac{9}{21}=-\frac{3}{7}\text{.}[/tex]
Replacing m = -3/7 and (x1, y1) = (-7, 7) in the general equation of the line, we have:
[tex]y=-\frac{3}{7}\cdot(x+7)+7.[/tex]
We can rewrite this equation in the following way:
[tex]\begin{gathered} y-7=-\frac{3}{7}\cdot(x+7), \\ -\frac{7}{3}\cdot(y-7)=x+7, \\ x=-\frac{7}{3}\cdot(y-7)-7. \end{gathered}[/tex]
Answer
The equation of the line is:
[tex]\begin{gathered} x=-\frac{7}{3}\cdot(y-7)-7 \\ x=-\frac{7}{3}\cdot(y+2)+14 \end{gathered}[/tex]
