Question

Find the x- and y-intercepts of the equation 5y−8x=−8(5+x).

a) x-intercept: (−8,0), y-intercept: (0,5)
b) x-intercept:(−5,0), y-intercept: (0,−8)
c) x-intercept:(0,−8), y-intercept: (−5,0)
d) x-intercept: (0,5), y-intercept: (−8,0)

Answer 1

To find the x-intercept of the equation, set y to 0 and solve for x; for the y-intercept, set x to 0 and solve for y. The x-intercept is (5, 0) and the y-intercept is (0, -8), indicating option b as the correct answer.

Step-by-step explanation:

The student is asking to find the x- and y-intercepts of the equation 5y−8x=−8(5+x). To find the x-intercept, we set y to 0 and solve for x; to find the y-intercept, we set x to 0 and solve for y.

1. To find the x-intercept, substitute y with 0:
2. 5(0) - 8x = -8(5 + 0)
3. 
   
4. → -8x = -40
5. 
   
6. → x = 5
7. To find the y-intercept, substitute x with 0:
8. 5y - 8(0) = -8(5 + 0)
9. 
   
10. → 5y = -40
11. 
    
12. → y = -8

The x-intercept is (5, 0) and the y-intercept is (0, -8), so the correct answer is option b: x-intercept:(−5,0), y-intercept: (0,−8).