Question

8-42. mary says that you can find an x-intercept by substituting 0 for x, while michelle says that you need to substitute 0 for y.

a. who, if anyone, is correct and why?

b. use the correct approach to find the x-intercept of -4x + 5y = 16.

Explanation:

Step1: Define x-intercept

An x-intercept is a point $(x, 0)$ where the graph crosses the x-axis, so $y=0$.

Step2: Evaluate Mary/Michelle's claim

Mary substitutes $x=0$ (finds y-intercept), Michelle substitutes $y=0$ (matches x-intercept definition).

Step3: Substitute $y=0$ into equation

For $-4x + 5y = 16$, substitute $y=0$:
$-4x + 5(0) = 16$

Step4: Solve for x

Simplify and isolate $x$:
$-4x = 16$
$x = \frac{16}{-4} = -4$

Answer:

a. Michelle is correct. The x-intercept is the point where the graph crosses the x-axis, which occurs when $y=0$, so substituting 0 for $y$ is the correct method. Substituting 0 for $x$ finds the y-intercept, not the x-intercept.
b. The x-intercept is $(-4, 0)$ (or $x=-4$)