Question

question 1 (1 point)
(02.05 mc)
given the function f(x) = 4x + 10 and g(x), which function has a greater slope?

x	g(x)
2	5
4	7
6	9

a f(x) has a greater slope.
b g(x) has a greater slope.
c the slopes of f(x) and g(x) are the same.
d the slope of g(x) is undefined.

Explanation:

Step1: Find the slope of f(x)

The function $f(x)=4x + 10$ is in the form $y=mx + b$ where $m$ is the slope. So the slope of $f(x)$ is $m_f=4$.

Step2: Find the slope of g(x)

Use the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(2,5)$ and $(x_2,y_2)=(4,7)$. Then $m_g=\frac{7 - 5}{4 - 2}=\frac{2}{2}=1$.

Step3: Compare the slopes

Since $4>1$, $m_f>m_g$.

Answer:

A. f(x) has a greater slope