We are asked to find the linear equation of a line that passes through the points (0,-10) and (-10,2). To do that, let's remember the general form of a line equation:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" the y-intercept. To determine the slope we use the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In our case we have:
[tex]\begin{gathered} (x_1,y_1)=(0,-10) \\ (x_2,y_2)=(-10,2) \end{gathered}[/tex]Replacing in the equation for the slope:
[tex]m=\frac{2-(-10)}{-10-0}[/tex]Solving the operations:
[tex]m=\frac{2+10}{-10}=\frac{12}{-10}=-\frac{6}{5}[/tex]We replace the value of the slope in the general equation for the line:
[tex]y=-\frac{6}{5}x+b[/tex]Now we need to replace one of the given points in order to find the y-intercept "b". We will use the point (x,y) = (0,-10). This means that when x = 0, y = -10:
[tex]-10=-\frac{6}{5}(0)+b[/tex]Solving the operations we get:
[tex]-10=b[/tex]We replace the value of "b" in the general equation for the line:
[tex]y=-\frac{6}{5}x-10[/tex]And thus we find the linear equation.
