Q:

# Braden bought 18 pencils for \$4.50.Let x represent the number of pencils purchased, and let y represent the total cost.Graph the line that represents the proportional relationship.

Accepted Solution

A:
AnswerTo 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. ExplanationNotice 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:
$$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$$
where Β $$m$$ is the slope of the line
$$(x_{1},y_{1})$$ are the coordinates of the first point on the line
$$(x_{2},y_{2})$$ are the coordinates of the second point Since we already have our two points, we can replace the values in our formula:$$m=\frac{4.5-0}{18-0}$$
$$m=\frac{4.5}{18}$$
$$m=\frac{4.5-0}{18-0}$$
$$m=0.25$$Now that we have our slope, we can use the point slope formula to complete the equation of our line: $$y-y_{1}=m(x-x_{1})$$$$y=0.25x$$Now, to graph the line that represents the proportional relationship, we will join the points (0, 0) and (18, 4.5) using our line.