We must plot three points for the line and graph it, for the line we know, a point and its slope, which are:
[tex]\begin{gathered} (-4,2) \\ m=-\frac{1}{3} \end{gathered}[/tex]To do this we first determine the function that describes this line, with the form y=mx+b where "y", we know it at a point being 2, "x" is -4 and m is the slope, now we clear b
[tex]\begin{gathered} 2=-\frac{1}{3}\cdot(-4)+b \\ 2=\frac{4}{3}+b \\ b=2-\frac{4}{3} \\ b=\frac{2}{3} \end{gathered}[/tex]So our function is as follows:
[tex]y=-\frac{1}{3}x+\frac{2}{3}[/tex]Having the function, we can now collect values for "x" and find the points to solve for and find the "y" value, in this case, we use x=-1, x=0, and x=2.
These values are random, they can be any desired value.
[tex]\begin{gathered} x=-1 \\ y=-\frac{1}{3}\cdot(-1)+\frac{2}{3} \\ y=\frac{1}{3}+\frac{2}{3} \\ y=1 \end{gathered}[/tex]The first point is (-1,1)
[tex]\begin{gathered} x=0 \\ y=-\frac{1}{3}\cdot0+\frac{2}{3} \\ y=\frac{2}{3} \end{gathered}[/tex]The second point is (0,2/3)
[tex]\begin{gathered} x=2 \\ y=-\frac{1}{3}\cdot(2)+\frac{2}{3} \\ y=-\frac{2}{3}+\frac{2}{3} \\ y=0 \end{gathered}[/tex]The third point is (2,0)
In conclusion the points are:
[tex]\begin{gathered} (-1,1) \\ (0,\frac{2}{3}) \\ (2,0) \end{gathered}[/tex]Now, to plot this line, what we have to do is plot the points found and draw a line through all the points.
The graph with the given point, the three points found and your graph should look like the following graph.
