Question

8) Kyle has two jobs. He rakes leaves for hours at a rate of $2 an hour and is a student tutor for y hours ata rate of $5 an hour. This week, he earned $60.a) Write an equation to represent the situation.20b) Graph the equation on the set of axes.101020c) Determine and state one combination of hours that Kyle could have worked to earn $60.

Answer 1

a)

x represents the number of ours he raked leafs, if he gets paid $2 per hour, then his earnings from it can be expressed as: 2x

y represents the number of hours he tutors, if he gets paid $5 per hour, then his earnings from tutoring can be expressed as: 5y

If T represents his total earnings, you can calculate it by adding the amount of hours worked raking leafs multiplied by the hourly wage plus the amount of hours worked tutoring mutiplied by the hourly wage:

`T=2x+5y`

He earned $60 in a week, for this amount the equation is

`60=2x+5y`

b) and c)

To draw the line you need to determine two points it passes through, this points will also indicate a combination of hours that Kyle may have worked to earn those $60

To plot the line is best to express the equation in slope-intercept form:

`\begin{gathered} 60=2x+5y \\ 60-2x=5y \\ (60)/(5)-(2x)/(5)=(5y)/(5) \\ 12-(2)/(5)x=y \\ \to y=-(2)/(5)x+12 \end{gathered}`

From this equation you can determine two points of the line and graph it.

The easiest point to find for a linear equation is the y-intercept, that is the point where the line crosses the y-axis.

For this point the value of x is always zero, replace it in the formula and you get that the y-intercept is

`\begin{gathered} y=-(2)/(5)0+12 \\ y=12 \end{gathered}`

The coordinates are (0,12) → This point can be interpreted as: Kyle has to work 12 hours tutoring to earn $60 without raking any leafs.

For the next point, choose a random value of x and replace it in the formula. I'll use x=4 (this value indicates that Kyle raked leafs for 4 hours during the week)

`\begin{gathered} y=-(2)/(5)x+12 \\ y=-(2)/(5)\cdot4+12 \\ y=-(8)/(2)+12 \\ y=10.4 \end{gathered}`

The point is (4,10.4) → You can interpret this combination as: Kyle has to work 4 hours raking leafs ans 10.4hours tutoring students to earn $60 a week.

Now that you have both points you can plot the line.