Question

a linear function is given. complete parts (a)-(d).
g(x) = 5x + 2

(a) determine the slope and y-intercept of the function.
the slope is \boxed{}.
(type an integer or a simplified fraction.)
the y-intercept is \boxed{}.
(type an integer or a simplified fraction.)
(b) use the slope and y-intercept to graph the linear function.
use the graphing tool to graph the function. use the slope and y-intercept when drawing the line.
click to enlarge graph (image of a line on coordinate plane)
(c) determine the average rate of change of the function.
the average rate of change is \boxed{}.
(d) determine whether the linear function is increasing, decreasing, or constant. choose the correct answer below.
\bigcirc a. increasing
\bigcirc b. decreasing
\bigcirc c. constant

Explanation:

Step1: Recall slope-intercept form

The slope - intercept form of a linear function is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. For the function \(g(x)=5x + 2\), we can compare it with \(y=mx + b\).

Step2: Find the slope

By comparing \(g(x)=5x + 2\) with \(y = mx + b\), we see that \(m = 5\). So the slope is \(5\).

Step3: Find the y - intercept

By comparing \(g(x)=5x + 2\) with \(y=mx + b\), we see that \(b = 2\). So the \(y\) - intercept is \(2\) (the point is \((0,2)\)).

Step4: Determine the average rate of change

For a linear function \(y=mx + b\), the average rate of change is equal to the slope \(m\). Since the slope \(m = 5\), the average rate of change is \(5\).

Step5: Determine if the function is increasing, decreasing, or constant

A linear function \(y = mx + b\) is increasing if \(m>0\), decreasing if \(m < 0\), and constant if \(m = 0\). Since \(m = 5>0\), the function is increasing.

Answer:

s:
(a) The slope is \(\boldsymbol{5}\). The \(y\) - intercept is \(\boldsymbol{2}\).
(c) The average rate of change is \(\boldsymbol{5}\).
(d) \(\boldsymbol{A}\). increasing