Question

the equation represents function a, and the graph represents function b: function a f(x)=x - 9 function b which equation best compares the slopes of the two functions? a slope of function b = 2 x slope of function a b slope of function a = slope of function b c slope of function a = 2 x slope of function b d slope of function b = - slope of function a

Explanation:

Step1: Find slope of Function A

The equation of Function A is $f(x)=x - 9$, which is in slope - intercept form $y=mx + b$ where $m$ is the slope. So the slope of Function A, $m_A=1$.

Step2: Find slope of Function B

Using two points on the graph of Function B, say $(0, - 1)$ and $(1,0)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Then $m_B=\frac{0-( - 1)}{1 - 0}=\frac{0 + 1}{1}=1$.

Step3: Compare slopes

Since $m_A = 1$ and $m_B=1$, we have slope of Function A = slope of Function B.

Answer:

B. Slope of Function A = Slope of Function B