Let's first write down all the information given in y = mx + b form. Notice that x-intercept means that y = 0 at that point. b is not given, so:
[tex]0 = -3(15) + b[/tex]
Let's solve for b:
[tex]0 = -45+b[/tex]
[tex]b = 45[/tex]
Now we have the equation:
[tex]y = -3x + 45[/tex]
We can plug in every option given to see which choice makes it true:
(0, 30)
[tex]30 = -3(0) + 45[/tex]
[tex]30 \neq 45[/tex]
(5, 15)
[tex]15 = -3(5) + 45[/tex][tex]15 = -15+45[/tex]
[tex]15\neq 30[/tex]
(10, 10)
[tex]10 = -3(10) + 45[/tex]
[tex]10 \neq 15[/tex]
(-5, 60)
[tex]60 = -3(-5) + 45[/tex]
[tex]60 = 60[/tex]
Therefore, choice D or (-5, 60) is your answer. Hope I could help! :)
*There is probably an easier way to solve this, I just didn't see it when I attacked the problem! :)
