Question

1. find the unit rate in each graph and give the point that represents the unit rate.

a.

b.

c.

Explanation:

Step1: Recall the formula for unit rate

The unit rate \(r\) for a relationship \(y = rx\) (where \(y\) is the dependent variable and \(x\) is the independent variable) can be found using the formula \(r=\frac{y}{x}\). For a graph passing through the origin \((0,0)\), the unit rate is the slope of the line. The slope \(m\) of a line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). When \(x_1 = 0\) and \(y_1=0\), \(m=\frac{y}{x}\) for any non - origin point \((x,y)\) on the line. The unit rate is represented by the point \((1,r)\)

Step2: Analyze Graph A

Assume two points on the line: \((0,10)\) and \((10,100)\). The slope \(m=\frac{100 - 10}{10-0}=\frac{90}{10}=9\). The unit rate is \(9\) dollars per book. The point representing the unit rate is \((1,9)\)

Step3: Analyze Graph B

We have the point \((1,2.5)\). Using the formula \(r=\frac{y}{x}\), when \(x = 1\) and \(y=2.5\), the unit rate \(r = 2.5\) dollars per pound of potato salad. The point representing the unit rate is \((1,2.5)\)

Step4: Analyze Graph C

Take the point \((2,150)\). Using the formula \(r=\frac{y}{x}\), \(r=\frac{150}{2}=75\). The unit rate is \(75\) miles per hour. The point representing the unit rate is \((1,75)\)

Answer:

• Graph A: Unit rate is \(9\) dollars per book, point \((1,9)\)
• Graph B: Unit rate is \(2.5\) dollars per pound of potato salad, point \((1,2.5)\)
• Graph C: Unit rate is \(75\) miles per hour, point \((1,75)\)