Answer: (-12,-6)
Step-by-step explanation:
If we already have two points of the line, we can find its slope ([tex]m[/tex]), its intersection with the y-axis ([tex]b[/tex]), hence its equation:
Point 1: [tex](x_{1},y_{1})=(3,0)[/tex]
Point 2: [tex](x_{2},y_{2})=(-2,-2)[/tex]
Slope equation:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{-2-0}{-2-3}[/tex]
[tex]m=\frac{2}{5}[/tex] This is the slope of the line
Now, the equation of the line is:
[tex]y=mx+b[/tex]
We already know the slope, now we have to find [tex]b[/tex] with any of the given points. Let's choose Point 1: [tex](x_{1},y_{1})=(3,0)[/tex]
[tex]0=\frac{2}{5}(3)+b[/tex]
Isolating [tex]b[/tex]:
[tex]b=-\frac{6}{5}[/tex]
Then, the equation of the line is:
[tex]y=\frac{2}{5} x-\frac{6}{5}[/tex]
With this equation we can find which point is a solution. Let's begin with the first point (-12,-6):
[tex]-6=\frac{2}{5} (-12)-\frac{6}{5}[/tex]
[tex]-6=-\frac{24}{5} -\frac{6}{5}[/tex]
[tex]-6=-6[/tex] Since both sides of the equation are equal, (-12,-6) is the point that fulfills the solution of the equation.
