Given: The point and the slope below
[tex]\begin{gathered} Point:(18,-5) \\ slope=-8 \end{gathered}[/tex]To Determine: The equation o fthe line passing through the given point and slope
Solution
The formula for finding the equation of a line passing through a point and slope is
[tex]\begin{gathered} Point:(x_1,y_1) \\ Slope=m \\ \frac{y-y_1}{x-x_1}=m \end{gathered}[/tex]Substitute the given into the formula
[tex]\begin{gathered} \frac{y--5}{x-18}=-8 \\ \frac{y+5}{x-18}=-8 \end{gathered}[/tex][tex]\begin{gathered} y+5=-8(x-18) \\ y+5=-8x+144 \\ y+8x=144-5 \\ y+8x=139 \end{gathered}[/tex]Hence, the equation of the line passing through the given point and slope is
y + 8x = 139
