IDENTIFY AND SET UP
We are given the slope of a line and a point in which the same line passes through. We also know that the slope of a line can be obtained from the equation:
[tex]\begin{gathered} s=\frac{y-y_1}{x-x_1} \\ \text{ where:} \\ (x_1,y_1)=\text{ point that line passed through.} \\ s=\text{slope} \end{gathered}[/tex]
Our approach is to employ the formula above by substitute our coordinates.
EXECUTE
[tex]\begin{gathered} -5=\frac{y-(-10)}{x-3} \\ \text{ Cross multiplying, we get:} \\ -5x+15=y+10 \\ \text{Subtract 10 from both sides to get:} \\ y=-5x+15-10 \\ y=-5x+5 \end{gathered}[/tex]
The equation of our line is y = -5x + 5
