Answer:
[tex]Ratio = \frac{3}{2}[/tex]
Step-by-step explanation:
See attachment for complete question.
We start by solving for the equation of the graph (The graph shows a linear equation)
Represent pencils with x and pen with y
From the graph, we have that:
[tex](x_1,y_1) = (6,4)[/tex]
[tex](x_2,y_2) = (12,8)[/tex]
Solve for slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{8 - 4}{12- 6}[/tex]
[tex]m = \frac{4}{6}[/tex]
[tex]m = \frac{2}{3}[/tex]
The equation is calculated using:
[tex]y - y_1 = m(x - x_1)[/tex]
Where
[tex]m = \frac{2}{3}[/tex]
[tex](x_1,y_1) = (6,4)[/tex]
[tex]y - 4 = \frac{2}{3}(x - 6)[/tex]
[tex]y - 4 = \frac{2}{3}x - \frac{2}{3} * 6[/tex]
[tex]y - 4 = \frac{2}{3}x - \frac{2 * 6}{3}[/tex]
[tex]y - 4 = \frac{2}{3}x - \frac{12}{3}[/tex]
[tex]y - 4 = \frac{2}{3}x - 4[/tex]
Add 4 to both sides
[tex]y - 4 +4= \frac{2}{3}x - 4 + 4[/tex]
[tex]y= \frac{2}{3}x[/tex]
Now, to the question.
When pencils is 15 implies that
[tex]x = 15[/tex]
Solving for x, we have:
[tex]y= \frac{2}{3}x[/tex]
[tex]y= \frac{2}{3} * 15[/tex]
[tex]y= \frac{2* 15}{3}[/tex]
[tex]y= \frac{30}{3}[/tex]
[tex]y= 10[/tex]
i.e. Pen = 10
Ratio = x ; y
[tex]x : y = 15 : 10[/tex]
Convert to fraction
[tex]\frac{x}{y} = \frac{15}{10}[/tex]
Simplify
[tex]\frac{x}{y} = \frac{3}{2}[/tex]
Hence,
[tex]Ratio = \frac{3}{2}[/tex]
