Question

1. find the unit rate from this graph.
2. write an algebraic equation for the following table:

x	y
2	14
5	23
9	35
11	41

Explanation:

Question 8:

Step1: Identify two points

From the graph, we can take the points \((1, 15)\) and \((2, 30)\) (or any other two points like \((6, 45)\) and \((8, 60)\)).

Step2: Calculate the unit rate

The unit rate is the slope, which is \(\frac{\text{change in miles}}{\text{change in hours}}\). Using the points \((1, 15)\) and \((2, 30)\), the change in miles is \(30 - 15 = 15\) and the change in hours is \(2 - 1 = 1\). So the unit rate is \(\frac{15}{1}=15\) miles per hour.

Step1: Find the slope (\(m\))

We use the formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take the points \((2, 14)\) and \((5, 23)\). Then \(m=\frac{23 - 14}{5 - 2}=\frac{9}{3} = 3\).

Step2: Find the y - intercept (\(b\))

We use the equation \(y=mx + b\). Substitute \(x = 2\), \(y = 14\) and \(m = 3\) into the equation: \(14=3\times2 + b\). So \(14 = 6 + b\), and \(b=14 - 6=8\).

Step3: Write the equation

Using \(y=mx + b\) with \(m = 3\) and \(b = 8\), the equation is \(y = 3x+8\).

Answer:

The unit rate is 15 miles per hour.

Question 10: