Answer
To graph the line of the proportional relationship you should plot the points (0, 0) and (18, 4.5), and then join the points with a line.
Explanation
Notice that is pretty obvious that 0 pencils cost 0 dollars, so our fist point will be (0, 0). Since x represent the number of pencils purchased and y the total cost, our second point will be (18, 4.5)
Now we can find the slope of our line using the point slope formula:
slope formula:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
where
[tex]m[/tex] is the slope of the line
[tex](x_{1},y_{1})[/tex] are the coordinates of the first point on the line
[tex](x_{2},y_{2})[/tex] are the coordinates of the second point
Since we already have our two points, we can replace the values in our formula:
[tex]m=\frac{4.5-0}{18-0}[/tex]
[tex]m=\frac{4.5}{18}[/tex]
[tex]m=\frac{4.5-0}{18-0}[/tex]
[tex]m=0.25[/tex]
Now that we have our slope, we can use the point slope formula to complete the equation of our line:
[tex]y-y_{1}=m(x-x_{1})[/tex]
[tex]y=0.25x[/tex]
Now, to graph the line that represents the proportional relationship, we will join the points (0, 0) and (18, 4.5) using our line.
