Question

(02.05 mc)
the equation represents function a, and the graph represents function b:
function a
f(x)= - 2x + 1
function b

which equation best compares the slopes of the two functions? (1 point)
slope of function b = 2 x slope of function a
slope of function a = slope of function b
slope of function a = 2 x slope of function b
slope of function b = - slope of function a

Explanation:

Step1: Find slope of Function A

The equation of Function A is $f(x)=- 2x + 1$, which is in slope - intercept form $y = mx + b$ where $m$ is the slope. So the slope of Function A, $m_A=-2$.

Step2: Find slope of Function B

Using two points on the graph of Function B, say $(0, - 3)$ and $(3,3)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Then $m_B=\frac{3-( - 3)}{3 - 0}=\frac{6}{3}=2$.

Step3: Compare the slopes

We have $m_B = 2$ and $m_A=-2$, so $m_B=-m_A$.

Answer:

Slope of Function B = - Slope of Function A