Question

function a is a linear function. an equation for function a is $y = -\frac{3}{2}x + -6$. function b is a linear function whose graph includes the points (4, -12) and (-2, 0). compare the functions by completing the sentences. greater than equal to less than the slope of function a is the slope of function b. the x-intercept of function a is the x-intercept of function b.

Explanation:

Step1: Find slope of Function B

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. For points $(4, -12)$ and $(-2, 0)$, $m = \frac{0 - (-12)}{-2 - 4} = \frac{12}{-6} = -2$.

Step2: Compare slopes of A and B

Slope of Function A is $-\frac{3}{2} = -1.5$. Since $-1.5 > -2$, slope of A is greater than slope of B.

Step3: Find x - intercept of Function A

Set $y = 0$ in $y = -\frac{3}{2}x - 6$. So $0 = -\frac{3}{2}x - 6$. Add 6 to both sides: $6 = -\frac{3}{2}x$. Multiply both sides by $-\frac{2}{3}$: $x = -4$.

Step4: Find x - intercept of Function B

From points, when $y = 0$, $x = -2$.

Step5: Compare x - intercepts

$-4 < -2$, so x - intercept of A is less than that of B.

Answer:

The slope of Function A is greater than the slope of Function B. The x - intercept of Function A is less than the x - intercept of Function B.