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

1 Typing speed ★★★

Maya types 135 words in 3 minutes at a steady pace.

1. Find her unit rate in words per minute.
2. How many words can she type in 8 minutes?

2 Smoothie prices ★★★

Four cups of smoothie cost $10.00 at the juice bar, and the price is proportional to the number of cups.

Find the price per cup, then complete the table.

3 Proportional or not? ★★★

Tell whether each set of ordered pairs is proportional, and justify.

1. \((2, 6), (4, 12), (5, 15)\)
2. \((1, 3), (2, 5), (3, 7)\)

4 Reading a slope ★★★

The line below passes through \(A(2, 3)\) and \(B(6, 9)\). Find its slope using the rise and the run.

5 Two points ★★★

Find the slope of the line through \((1, 2)\) and \((4, 11)\).

6 Highway speed ★★★

A car drives 150 miles in 2.5 hours at a constant speed. Find the speed in miles per hour, then convert it to kilometers per hour (1 mile \(\approx\) 1.609 km).

7 Plotting y = 2x ★★★

Complete the table for \(y = 2x\) with \(x = 0, 1, 2, 3\), plot the points, and state the slope of the line.

8 A steep negative slope ★★★

Find the slope of the line through \((-3, 4)\) and \((5, -8)\), and say whether the line rises or falls from left to right.

9 Horizontal and vertical ★★★

Find the slope of the line through each pair of points, or explain why it does not exist.

1. \((2, 5)\) and \((7, 5)\)
2. \((3, -1)\) and \((3, 6)\)

10 Apple prices ★★★

Store A sells 5 pounds of apples for $9.00. At Store B the cost \(y\) in dollars for \(x\) pounds is \(y = 1.95x\).

1. Which store has the lower price per pound?
2. How much do you save by buying 12 pounds at the cheaper store?

11 A draining tank ★★★

A water tank holds 60 gallons at time 0. After 8 minutes it holds 36 gallons. Use the points \((0, 60)\) and \((8, 36)\).

1. Find the slope and explain what it means.
2. Is the relationship proportional? Why?
3. If the pace stays the same, when will the tank be empty?

12 A missing coordinate ★★★

A proportional relationship has a graph through \((0, 0)\) and \((4, 10)\). The point \((6, k)\) is also on the line. Find the slope and the value of \(k\).

13 Equation from a table ★★★

The table shows a proportional relationship. Find the constant of proportionality and write the equation.

14 Running pace ★★★

Jordan runs 6 kilometers in 40 minutes at a steady pace. Find the unit rate in kilometers per hour, then in miles per hour (1 mile \(\approx\) 1.609 km, round to the nearest tenth).

15 Similar triangles on a line ★★★

Two right triangles are drawn under the same line through the origin: the small one has run 4 and rise 3; the large one has run 12 and rise 9.

1. Show that both triangles give the same slope.
2. A third triangle on this line has run 20. What is its rise?

16 Wheelchair ramp ★★★

A ramp rises 2.5 feet over a horizontal distance of 30 feet.

1. Find the slope as a fraction in simplest form.
2. A second ramp with the same slope must rise 1.5 feet. How long is its horizontal run?

17 Find the unknown ★★★

The line through \((2, k)\) and \((6, 13)\) has slope 2.5. Find \(k\).

18 Two sprinklers ★★★

Sprinkler 1 delivers 8 gallons in 5 minutes. For Sprinkler 2, the gallons \(g\) after \(t\) minutes satisfy \(g = 1.7t\). Both are proportional.

1. Compare their slopes.
2. How many gallons does each deliver in 20 minutes?

19 Collinear points ★★★

Points \(A(-1, -2)\), \(B(2, 4)\), \(C(5, 10)\) and \(D(8, 15)\) are given.

1. Show that \(A\), \(B\) and \(C\) lie on the same line.
2. Does \(D\) lie on that line?

20 Find the error ★★★

A student finds the slope through \((1, 3)\) and \((5, 11)\) and writes \(m = \dfrac{5 - 1}{11 - 3} = \dfrac{4}{8} = 0.5\). Explain the error and give the correct slope.

21 Two printers ★★★

Printer A prints 90 pages in 6 minutes. Printer B’s graph is a line through \((0, 0)\) and \((4, 64)\), where the point means 64 pages in 4 minutes. Working together at these steady rates, how long do they need to print 465 pages?