Answer
(a) slope is $-4$; $y$-intercept is $3$
(b) $-4$
(c) decreasing (because the slope is negative)
(d) Refer to the graph below.
Work Step by Step
We are given the function:
$f(x)=-4x+3$
a) Find the slope using the form $y=mx+b$ where the slope is $m$ and the $y$-intercept is $b$.:
$m=-4$
Determine the $y$-intercept:
$b=3$
b) Determine the average rate of change of $f$:
$\dfrac{\Delta y}{\Delta x}=m=-4$
c) Since the slope is negative, then the function is decreasing.
d) The intercepts are:
$y$-intercept: $3$
$x$-intercept: $-4x+3=0\Rightarrow x=\dfrac{3}{4}$
Graph the function by plotting the intercepts $(0, 3)$ and $\left(\frac{3}{4}, 0\right)$ and connecting the points using a line.
