Question

5
ounces
pieces
2 miles per hour
6
dollars
tickets
grade 8 • lesson 8 page 1 of

Explanation:

Step1: Analyze Graph 5

To find the rate (slope) for Graph 5, we use the formula for slope \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Take two points, say \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(11, 3.5)\) (approximate from the graph). Wait, better to take a clear point. Let's take \((8, 2)\) (since at \(x = 8\) pieces, \(y=2\) ounces). So slope \(m=\frac{2 - 0}{8 - 0}=\frac{2}{8}=\frac{1}{4}=0.25\) ounces per piece. Wait, maybe another point. Wait, the y - axis is ounces, x - axis is pieces. Let's take \(x = 4\), \(y = 1\). Then slope \(m=\frac{1-0}{4 - 0}=\frac{1}{4}=0.25\) ounces per piece.

Step2: Analyze Graph 6

For Graph 6, x - axis is tickets, y - axis is dollars. Take two points \((0,0)\) and \((5, 100)\) (wait, no, at \(x = 5\), y is around 100? Wait, no, looking at the grid, each square is, say, 10 dollars? Wait, no, let's take \(x = 2\), \(y = 40\) (since at \(x = 2\) tickets, \(y = 40\) dollars). Then slope \(m=\frac{40-0}{2 - 0}=20\) dollars per ticket. Wait, maybe the problem is to find the unit rate (slope) for each graph. But the original problem's first part says "2 miles per hour" (maybe a typo, "miles" should be related? Wait, the user's image has two graphs, 5 and 6. Let's assume we need to find the rate for each.

Wait, maybe the first graph (Graph 5) has a rate of \( \frac{1}{4} \) ounces per piece (since 1 ounce at 4 pieces: \( \frac{1}{4} \) oz per piece). Graph 6: at \(x = 1\) ticket, \(y = 20\) dollars? Wait, no, at \(x = 5\) tickets, \(y = 100\) dollars? Wait, the graph 6: when x=5, y is at the top, maybe 100? Wait, no, the y - axis is from 0 to 100, x from 0 to 10. Let's take x=2, y=40 (since 2 tickets, 40 dollars). So rate is \( \frac{40}{2}=20 \) dollars per ticket.

But maybe the original question (since the user's image has "2 miles per hour" written, maybe a previous problem, and now graphs 5 and 6. Let's re - check.

Wait, the first graph (Graph 5): x is pieces, y is ounces. Let's take x = 8, y = 2. So rate is \( \frac{2}{8}=0.25 \) ounces per piece.

Graph 6: x is tickets, y is dollars. Let's take x = 5, y = 100 (assuming the line goes to (5,100)). Then rate is \( \frac{100}{5}=20 \) dollars per ticket.

But maybe the problem is to find the unit rate (slope) for each graph. Let's proceed.

Wait, the user's initial text has "2 mikes per hour" (typo, "miles" or "mikes"? Maybe a typo. Let's assume we need to find the rate for each graph.

For Graph 5 (Pieces vs Ounces):

• Pick two points: \((0,0)\) and \((4,1)\) (since at \(x = 4\) pieces, \(y = 1\) ounce).
• Slope (rate) \(m=\frac{1 - 0}{4 - 0}=\frac{1}{4}=0.25\) ounces per piece.

For Graph 6 (Tickets vs Dollars):

• Pick two points: \((0,0)\) and \((2,40)\) (since at \(x = 2\) tickets, \(y = 40\) dollars).
• Slope (rate) \(m=\frac{40 - 0}{2 - 0}=20\) dollars per ticket.

But since the problem is not fully stated, but assuming we need to find the rate for each graph, we can calculate as above.

Answer:

For Graph 5: \(0.25\) ounces per piece; For Graph 6: \(20\) dollars per ticket.

(Note: Since the original problem's exact question is not clear from the image, this is a best - effort based on the graphs. If the question was different, adjust accordingly.)