MATH SOLVE

3 months ago

Q:
# (Please Hurry!!) 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. (Please tell me what points I should plot! Will mark Brainliest!!!)

Accepted Solution

A:

AnswerYou should plot the points (0, 0) and (18, 4.50)Explanation We know that zero pencils cost zero dollars, so our first point is (0, 0). We also know that 18 pencils cost 4.50; since [tex]x[/tex] is the number of pencils and [tex]y[/tex] the cost, our second point is (18, 4.50).Now let's find the equation and the graph of our line. But first, we are going to find the slope of our line using the 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 From our points we can infer that [tex]x_{1}=0[/tex], [tex]y_{1}=0[/tex], [tex]x_{2}=18[/tex], and [tex]y_{2}=4.50[/tex], so let's replace the values in our slope formula:[tex]m=\frac{4.50-0}{18-0}[/tex]

[tex]m=\frac{4.50}{18}[/tex]

[tex]m=0.25[/tex]The slope of our line means that each pencils costs $0.25 by the way.Now that we have the slope of our line, we can use the point slope formula to complete our line equation: [tex]y-y_{1}=m(x-x_{1})[/tex][tex]y-0=0.25(x-0)[/tex][tex]y=0.25x[/tex]We can conclude that we should plot the points (0, 0) and (18, 4.50) to graph the line [tex]y=0.25x[/tex] as shown in the picture.

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 From our points we can infer that [tex]x_{1}=0[/tex], [tex]y_{1}=0[/tex], [tex]x_{2}=18[/tex], and [tex]y_{2}=4.50[/tex], so let's replace the values in our slope formula:[tex]m=\frac{4.50-0}{18-0}[/tex]

[tex]m=\frac{4.50}{18}[/tex]

[tex]m=0.25[/tex]The slope of our line means that each pencils costs $0.25 by the way.Now that we have the slope of our line, we can use the point slope formula to complete our line equation: [tex]y-y_{1}=m(x-x_{1})[/tex][tex]y-0=0.25(x-0)[/tex][tex]y=0.25x[/tex]We can conclude that we should plot the points (0, 0) and (18, 4.50) to graph the line [tex]y=0.25x[/tex] as shown in the picture.