# Chapter 4 - Section 4.1 - Properties of Linear Functions and Linear Models - 4.1 Assess Your Understanding - Page 280: 14

(a) Slope $= 5$ and y-intercept $=-4$ (b) See the image. (c) Average rate of change $= 5.0$ (d) The linear function $g(x)=5x-4$ is increasing. Step-1: Compare the given equation with the point-slope form of the linear equation, that is, $g(x) = mx+b$, where $m$ is the slope of the linear function and $b$ is its y-intercept. By comparing $$g(x)=5x-4$$ to $$g(x) = mx+b$$ we understand that the slope of the given function is $5$ and its y-intercept is $-4$. Step-2: Let us put values of $x$ from $-2$ to $2$ into the function to obtain corresponding $y$ values. Using this we can plot a graph. Thus, For $x=-2$, $g(x)=-14$ For $x=-1$, $g(x)=-9$ For $x=0$, $g(x)=-4$ For $x=1$, $g(x)=1$ For $x=2$, $g(x) = 6$ This data obtains the graph shown. Step-3: The average rate of change is defined as follows: $$\frac{\Delta y}{\Delta x}=\frac{g(x_2)-g(x_1)}{x_2-x_1}$$ Let us calculate the average rate of change between $x_2=2$ and $x_1=-2$, $$\frac{\Delta y}{\Delta x}=\frac{6-(-14)}{2-(-2)}=5$$ Step-4: Since slope, $m=5>0$, this linear function is increasing. 