Question

function a
the y - intercept of function a is farther from the origin than the y - intercept of function b.
the slope of function a is less steep than the slope of function b.
the y - intercepts of the functions have opposite signs.
the slope of each function is negative.
function b

Explanation:

Step1: Find slope and y - intercept of Function A

Use the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$ with two points from the table of Function A, say $(x_1,y_1)=(-6,-5)$ and $(x_2,y_2)=(-2,-3)$. Then $m_A=\frac{-3-(-5)}{-2 - (-6)}=\frac{-3 + 5}{-2+6}=\frac{2}{4}=\frac{1}{2}$. Using the point - slope form $y - y_1=m(x - x_1)$ and the point $(-2,-3)$: $y+3=\frac{1}{2}(x + 2)$, which simplifies to $y=\frac{1}{2}x-2$, so the y - intercept of Function A is $b_A=-2$.

Step2: Find slope and y - intercept of Function B

From the graph of Function B, we can see that it passes through the points $(0, 8)$ and $(4,0)$. Using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, we have $m_B=\frac{0 - 8}{4-0}=\frac{-8}{4}=-2$. The y - intercept of Function B is $b_B = 8$.

Step3: Analyze each statement

• For the statement "The y - intercept of function A is farther from the origin than the y - intercept of function B": $|b_A|=2$ and $|b_B| = 8$, so this is false.
• For the statement "The slope of function A is less steep than the slope of function B": $|m_A|=\frac{1}{2}$ and $|m_B| = 2$, and $\frac{1}{2}<2$, so this is true.
• For the statement "The y - intercepts of the functions have opposite signs": $b_A=-2$ and $b_B = 8$, so this is true.
• For the statement "The slope of each function is negative": $m_A=\frac{1}{2}>0$ and $m_B=-2<0$, so this is false.

Answer:

The slope of function A is less steep than the slope of function B; The y - intercepts of the functions have opposite signs.