function a and function b are linear functions. function a: x y -10 -11 4 10 10 19 select all the statements…

Explanation:

Step1: Find the equation of Function A

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. The slope $m$ of Function A using two points $(x_1,y_1)=(-10,-11)$ and $(x_2,y_2)=(4,10)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{10+11}{4 + 10}=\frac{21}{14}=\frac{3}{2}$. Using the point - slope form $y - y_1=m(x - x_1)$ with the point $(4,10)$: $y-10=\frac{3}{2}(x - 4)$. Expanding gives $y-10=\frac{3}{2}x-6$, so $y=\frac{3}{2}x + 4$. The y - intercept of Function A is $b = 4$.

Step2: Find the y - intercept of Function B

From the graph of Function B, the line crosses the y - axis at the point $(0,0)$, so the y - intercept of Function B is $0$.

Step3: Find the y - value of Function A at $x=-4$

Substitute $x = - 4$ into $y=\frac{3}{2}x + 4$ of Function A: $y=\frac{3}{2}\times(-4)+4=-6 + 4=-2$.

Step4: Find the y - value of Function B at $x=-4$

From the graph of Function B, when $x=-4$, $y=-8$.

Answer:

The y - intercept of Function A is greater than the y - intercept of Function B; The y - value of Function A when $x=-4$ is greater than the y - value of Function B when $x=-4$. So the correct statements are: "The y - intercept of Function A is greater than the y - intercept of Function B".