Answer:
[tex](-\frac{50}{13},-\frac{12}{13})[/tex]
Step-by-step explanation:
To start, you need to find the equation of both of these lines. For the orange one, the slope can be found with the points (-5,0) and (0,-4), where there is a drop of 4 for a run of 5. This is a slope of -4/5, and a y-intercept of -4. For the purple line, you can use the points (-2,0) and (0,1), where there is a rise of 1 for a run of 2 or a slope of 1/2 and a y intercept of 1. Therefore, the two equations are:
[tex]y=-\frac{4}{5}x-4[/tex]
[tex]y=\frac{1}{2}x+1[/tex]
You can now set them equal to each other:
[tex]-\frac{4}{5}x-4=\frac{1}{2}x+1[/tex]
Add 4 to both sides:
[tex]-\frac{4}{5}x=\frac{1}{2}x+5[/tex]
Multiply both sides by 2:
[tex]-\frac{8}{5}x=x+10[/tex]
Multiply both sides by 5:
[tex]-8x=5x+50[/tex]
Subtract 5x from both sides:
[tex]-13x=50[/tex]
Divide both sides by -13:
[tex]x=-\frac{50}{13}[/tex]
[tex]y=-\frac{12}{13}[/tex]
Hope this helps!
