To plot two points on the graph of the given function [tex]\( p(x) = -4 - \frac{4}{3} x \)[/tex], we can follow these steps:
1. Identify Two Values for [tex]\( x \)[/tex]:
- Choose [tex]\( x = 0 \)[/tex]
- Choose [tex]\( x = 3 \)[/tex]
2. Calculate the Corresponding [tex]\( y \)[/tex]-Coordinates:
- For [tex]\( x = 0 \)[/tex]:
[tex]\[
p(0) = -4 - \frac{4}{3} \cdot 0 = -4
\][/tex]
So, the point is [tex]\((0, -4)\)[/tex].
- For [tex]\( x = 3 \)[/tex]:
[tex]\[
p(3) = -4 - \frac{4}{3} \cdot 3 = -4 - 4 = -8
\][/tex]
So, the point is [tex]\((3, -8)\)[/tex].
3. Summary of the Points:
- The first point is [tex]\((0, -4)\)[/tex]
- The second point is [tex]\((3, -8)\)[/tex]
By plotting these points on a coordinate plane, we get the points [tex]\((0, -4)\)[/tex] and [tex]\((3, -8)\)[/tex]. Connecting these points with a straight line will give you the graph of the function [tex]\( p(x) = -4 - \frac{4}{3} x \)[/tex].
Thus, the points you need to plot are:
[tex]\[
\begin{aligned}
&(0, -4), \\
&(3, -8)
\end{aligned}
\][/tex]
These correspond to the function [tex]\( p(x) = -4 - \frac{4}{3} x \)[/tex].
