linear functions a and b are represented by the table and graph shown. which statement is true about the…

Explanation:

Step1: Find slope of function A

Use slope - formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(-6,-5)$ and $(x_2,y_2)=(-2,-3)$. Then $m_A=\frac{-3-(-5)}{-2 - (-6)}=\frac{-3 + 5}{-2+6}=\frac{2}{4}=\frac{1}{2}$.

Step2: Find y - intercept of function A

Use point - slope form $y - y_1=m(x - x_1)$ with $m=\frac{1}{2}$ and $(x_1,y_1)=(-2,-3)$. $y+3=\frac{1}{2}(x + 2)$, expand to get $y+3=\frac{1}{2}x+1$, then $y=\frac{1}{2}x - 2$. So $y$-intercept of A is $b_A=-2$.

Step3: Find slope of function B

Pick two points on the graph of function B, say $(0, - 1)$ and $(-2,3)$. Then $m_B=\frac{3-(-1)}{-2 - 0}=\frac{4}{-2}=-2$.

Step4: Find y - intercept of function B

From the graph, the line of function B crosses the y - axis at $y=-1$, so $b_B=-1$.

Step5: Analyze each statement

• For the first statement: $|m_A|=\frac{1}{2}$ and $|m_B| = 2$, $\frac{1}{2}<2$, so the slope of function A is less steep than the slope of function B.
• For the second statement: $|b_A| = 2$, $|b_B|=1$, the $y$-intercept of function A is farther from the origin than the $y$-intercept of function B.
• For the third statement: $m_A=\frac{1}{2}>0$, the slope of function A is positive.
• For the fourth statement: $b_A=-2$ and $b_B=-1$, they have the same sign.

Answer:

The slope of function A is less steep than the slope of function B; The y - intercept of function A is farther from the origin than the y - intercept of function B.