Question

topic 2 linear relationships

1. jorge has a job delivering newspapers. each sunday, she earns $24.75 plus $0.20 for each house she delivers to.

a. write an equation that represents the amount jorge earns on sunday, y, given x number of houses she delivers to.
b. graph the equation.
c. identify the slope and y - intercept of the graph. explain what each means in terms of the situation.
d. jorge has earned $36.75 delivering newspapers. how many houses has she delivered to?

Explanation:

Step1: Determine the equation

The general form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\)-intercept. Here, the fixed amount (like a base pay) is \(b=\$24.75\) and the rate per house (slope) is \(m = 0.20\). So the equation is \(y=0.2x + 24.75\).

Step2: Graph the equation (description)

To graph \(y = 0.2x+24.75\), start by plotting the \(y\)-intercept at the point \((0,24.75)\). Then, use the slope \(m = 0.2=\frac{1}{5}\). From the \(y\)-intercept, move 1 unit up and 5 units to the right to find another point. Connect the points with a straight - line.

Step3: Identify slope and \(y\)-intercept

The slope \(m = 0.2\). In the context of the problem, it means that for each additional house Jorge delivers to, she earns an extra \(\$0.20\). The \(y\)-intercept \(b = 24.75\) means that if Jorge delivers to \(x = 0\) houses (the starting point), she still has \(\$24.75\) (maybe a base pay or a fixed amount for the job).

Step4: Solve for \(x\) when \(y = 36.75\)

Substitute \(y=36.75\) into the equation \(y = 0.2x+24.75\).

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Answer:

a. \(y = 0.2x+24.75\)
b. Graph with \(y\)-intercept \((0,24.75)\) and slope \(\frac{1}{5}\) (description as above)
c. Slope \(m = 0.2\) (earns \(\$0.20\) per house), \(y\)-intercept \(b = 24.75\) (base amount)
d. \(60\) houses