Question

Arlo is trying to find the x-intercept of 9x + 12y = 144. His work is shown below, 9x +12y = 144 9(0) + 12y =144 12y = 144 y = 12 The x-intercept is 12 1. Do you agree with Arlo's solution? If not, explain why. 2. Would another method for finding the x-intercept work well or even better? If so, explain. 3. How could you prove if Arlo's solution is correct or incorrect? 4. What would happen if 144 was negative? 5. How confident are you in your answers for the previous 4 questions? Explain.

Answer 1

Arlo's solution is incorrect

He has used the substitution x = 0 instead of y = 0 to find the x- intercept

To find the x-intercept let y = 0, in the equation and solve for x

y = 0 → 9x + 0 = 144

9x = 144 ( divide both sides by 9 )

x = $\frac{144}{9}$ = 16

the x- intercept is 16 ⇒ ( 16, 0 )

note to find the y-intercept let x = 0 in the equation and solve for y

x = 0 → 0 + 12y = 144

12y = 144 ⇒ y = 12

This is what Arlo calculated

If 144 was - 144 then x- intercept = - 16 and y-intercept = - 12