To graph the equation $y = \frac{7}{3}x$, you start by plotting the origin $(0, 0)$. What is the correct next step to find a second point using the slope?

From the origin, move up 7 units and right 3 units.

From the origin, move up 3 units and right 7 units.

From the origin, move to the point $(7, 0)$.

From the origin, move to the point $(0, 3)$.

Graphing Proportional Relationships Practice — Grade 8 math

Lesson 3: Graphing Proportional Relationships — Practice Questions

1. A proportional relationship is graphed passing through the point $(4, 20)$. Write the equation for this relationship in the form $y = mx$. The equation is $y = \text{\_\_\_}$.
2. Which equation represents a proportional relationship that passes through the point $(6, 18)$?
- A. $y = 3x$
- B. $y = \frac{1}{3}x$
- C. $y = 18x$
- D. $y = x + 12$
3. To graph the equation $y = \frac{7}{3}x$, you start by plotting the origin $(0, 0)$. What is the correct next step to find a second point using the slope?
- A. From the origin, move up 7 units and right 3 units.
- B. From the origin, move up 3 units and right 7 units.
- C. From the origin, move to the point $(7, 0)$.
- D. From the origin, move to the point $(0, 3)$.
4. A line representing a proportional relationship passes through the point $(5, 35)$. What is the constant of proportionality, $m$? $m = \text{\_\_\_}$.
5. The equation for a proportional relationship is $y = 6x$. Besides the origin, which of the following points lies on the graph of this equation?
- A. $(6, 1)$
- B. $(3, 18)$
- C. $(18, 3)$
- D. $(6, 6)$
6. A recipe's ingredient amounts are proportional to the number of servings. If a recipe for 4 servings needs 6 cups of flour, how many cups are needed for 10 servings? ___ cups
7. The total distance $d$ a train travels in $t$ hours is given by $d = 85t$. What is the constant of proportionality in this relationship?
- A. $d$
- B. $t$
- C. $85$
- D. $\frac{1}{85}$
8. The cost of gasoline is proportional to the number of gallons purchased. If 8 gallons of gasoline cost 28 dollars, what is the unit rate in dollars per gallon? ___ dollars
9. A printer can print 40 pages in 5 minutes. If the number of pages is proportional to the time, how many pages can it print in 12 minutes? ___ pages
10. In a proportional relationship where $y=rx$, if the value of $x$ is doubled, what happens to the value of $y$?
- A. It is halved.
- B. It is doubled.
- C. It increases by 2.
- D. It does not change.