Answer:
the desired x-intercept is (-53/5, 0); the y-intercept is (0, 53/3).
Explanation:
Find the equation of the line through the given points first:
As we move from (-7,6) to (-4,11), x increases by 3 and y by 5.
Thus, the slope of this line is m = rise / run = 5/3.
Use the slope-intercept formula y = mx + b. Substitute 5/3 for m, 6 for y and -7 for x:
6 = (5/3)(-7) + b, where b is the y-coordinate of the y-intercept:
6 = -35/3 + b, or 18/3 = -35/3 + b. Adding 35/3 to both sides, we get:
53/3 = b.
Then the y-intercept is (0, 53/3).
To find the x-intercept, let y = 0 and solve the resulting equatin for x:
0 = (5/3)x + 53/3, or 0 = 5x + 53. Then x = -53/5, and the desired x-intercept is (-53/5, 0).