Proportional Relationships and Slope: math test, Grade 8 – download the PDF

1 Unit rate / 3 pts

A drone flies 18 miles in 24 minutes at a steady speed.

1. Find its speed in miles per hour. (1 pt)
2. Write an equation giving the distance \(d\) after \(t\) hours. (1 pt)
3. How far does it fly in 2.5 hours? (1 pt)

2 Slope from two points / 4 pts

Let \(A(-4, 3)\), \(B(2, -9)\) and \(C(5, -15)\).

1. Find the slope of line \(AB\). (2 pts)
2. Show that \(C\) is on line \(AB\). (2 pts)

3 Reading a graph / 3 pts

Use the graph of a proportional relationship (the line passes through \((2, 3)\) and \((4, 6)\)).

1. Find the slope. (1 pt)
2. Write the equation of the line. (1 pt)
3. Find \(y\) when \(x = 10\). (1 pt)

4 Two faucets / 4 pts

Faucet A delivers 36 gallons in 8 minutes at a steady rate. For Faucet B, the gallons \(g\) after \(t\) minutes satisfy \(g = 4.2t\).

1. Find the rate of Faucet A. (1 pt)
2. Which faucet is faster? (1 pt)
3. How long does each need to deliver 63 gallons? (2 pts)

5 Similar triangles / 3 pts

A small right triangle under a line has run 8 and rise 10. A larger triangle under the same line has rise 35.

1. Find the slope of the line. (1 pt)
2. Explain why the two triangles are similar. (1 pt)
3. Find the run of the larger triangle. (1 pt)

6 True or false? / 3 pts

Decide and justify.

1. The pairs \((3, 12)\), \((5, 20)\), \((8, 32)\) are proportional. (1 pt)
2. The line through \((2, 6)\) and \((4, 9)\) is proportional. (1 pt)
3. The slope of the line through \((4, 7)\) and \((4, -2)\) is 0. (1 pt)