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 $(0, 3)$.

Proportional Relationships and Slope Practice — Grade 8 math

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. What is the slope of the line whose intercepts are $(-5, 0)$ and $(0, 3)$? ___
7. The population of a town was 4800 in 2005 and grew to 6780 by 2020. Assuming a constant rate of growth, what is the slope of the linear model for the population, representing the growth in people per year? ___