I'm here to help. Those 3 points all lie on the same line. We know this because if we find the slope between any 2 of those points, it is the same. I'll show you: [tex]m= \frac{12-20}{15-10}=- \frac{8}{5} [/tex]. Now another 2 points: [tex]m= \frac{4-12}{20-15}=- \frac{8}{5} [/tex]. The same holds for the first and third points. So we got that out of the way. Now we will pick any one of those points and use the x and y values and our slope to write an equation of that line and then finally solve for the x and y intercepts. I'm going to use the first point (10, 20): [tex]y-20=- \frac{8}{5}(x-10) [/tex]. We will simplify to get it into y = mx + b form: [tex]y-20=- \frac{8}{5}x+ \frac{80}{5} [/tex] and [tex]y-20=- \frac{8}{5}x+16 [/tex] and finally, [tex]y=- \frac{8}{5}x+36 [/tex]. The y-intercept exists when x = 0, so when x = 0, y = 36. The x-intercept exists when y = 0, so when y = 0, x = 22.5. In summary, y-intercept: (0, 36). x-intercept: (22.5, 0) and you're all done!
