Answer:
An equation of the line that passes through (-6,0) and (0,-24) is [tex]y=-4x-24[/tex]
Step-by-step explanation:
First, we need to determine the slope of the line. The formula for determining the slope of a line is:
[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
where m is the slope of the line and the x and y terms are for the points:
[tex](x_{1} , y_{1}) =(-6, 0)\\(x_{2} , y_{2}) =(0, -24)[/tex]
For this problem the slope is:
[tex]m=\frac{-24-0}{0-(-6)} \\m=\frac{-24}{6} \\m=-4[/tex]
Now, selecting one of the points we can use the point slope formula to find the equation.
The point slope formula is:
[tex]y -y_{1}=m(x -x_{1})[/tex]
Substituting one of our points gives:
[tex]y-0=-4(x-(-6))\\y=-4(x+6)\\y=-4x-24[/tex]
For more information:
https://brainly.com/question/9992092?referrer=searchResults
