Testinar Grade 8 math

Graphing Proportional Relationships

Learn to reason about and solve Grade 8 problems involving Graphing Proportional Relationships.

CH03-01 Equations, Inequalities, and Systems

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

A graph of a proportional relationship passes through the origin and \((5, 15)\). What is the slope (unit rate)?
1. \(2\)
2. \(15\)
3. \(5\)
4. \(3\)
What is the slope of the line shown in the graph?
1. \(\frac{1}{2}\)
2. \(6\)
3. \(3\)
4. \(2\)
What is the constant of proportionality for this graph?
1. \(\frac{1}{4}\)
2. \(4\)
3. \(2\)
4. \(\frac{1}{2}\)
Using the graph, find the equation of the proportional relationship.
1. \(y = 5x\)
2. \(y = \frac{5}{2}x\)
3. \(y = \frac{2}{5}x\)
4. \(y = 2x\)
What is the slope of the line?
1. \(2\)
2. \(16\)
3. \(8\)
4. \(4\)
Does the table show values from the equation \(y = 5x\)?
1. No, should be \(y = 5+x\)
2. No, should be \(y = x+5\)
3. Yes, each \(y\)-value is \(5\) times the matching \(x\)-value.
4. No, missing \(x=0\)
What is the unit rate shown in the graph?
1. \(3\) units of \(y\) per unit of \(x\)
2. \(2\) units of \(y\) per unit of \(x\)
3. \(\frac{1}{2}\) unit of \(y\) per unit of \(x\)
4. \(6\) units of \(y\) per unit of \(x\)
The graph shows a proportional relationship. Find the equation.
1. \(y = 9x\)
2. \(y = 3x\)
3. \(y = \frac{1}{3}x\)
4. \(y = x + 3\)

Teacher and parent reference

Answer key and explanations

D. \(3\)
Slope \(=\frac{\Delta y}{\Delta x}=\frac{15-0}{5-0}=3\). For a proportional line through the origin, the slope equals the unit rate.
D. \(2\)
Slope \(=\frac{\Delta y}{\Delta x}=\frac{6-0}{3-0}=\frac{6}{3}=2\). The line passes through \((0,0)\) and \((3,6)\).
D. \(\frac{1}{2}\)
Constant of proportionality \(k=\frac{y}{x}=\frac{2}{4}=\frac{1}{2}\). The line passes through \((0,0)\) and \((4,2)\).
C. \(y = \frac{2}{5}x\)
Slope \(k=\frac{2}{5}\). Equation: \(y=\frac{2}{5}x\).
D. \(4\)
Slope \(=\frac{8}{2}=4\). The line passes through \((0,0)\) and \((2,8)\).
C. Yes, each \(y\)-value is \(5\) times the matching \(x\)-value.
Each value: \(y=5(1)=5\), \(y=5(2)=10\), \(y=5(3)=15\). All match the equation \(y=5x\).
C. \(\frac{1}{2}\) unit of \(y\) per unit of \(x\)
Unit rate is slope: \(\frac{3}{6}=\frac{1}{2}\). For every 1 unit of \(x\), \(y\) increases by \(\frac{1}{2}\).
C. \(y = \frac{1}{3}x\)
Slope \(k=\frac{3}{9}=\frac{1}{3}\). Equation: \(y=\frac{1}{3}x\).