Question
Use the graph to answer the questions.
10, 50, 7, 35, 3, 15, 2, 10, 1, 5
a. The constant of proportionality is ______________
b. Write an equation that represents the linear graph. _______________
c. This is a proportional relationship because the graph shows ______________
Options: 2y = x, y = 5x, a constant rate of change, a linear relationship, 2, the points are connected, 5, linear with a y-intercept at (0, 0), 1/2, 1, 1/2y = x, 5y = x, 1/5
10, 50, 7, 35, 3, 15, 2, 10, 1, 5
a. The constant of proportionality is ______________
b. Write an equation that represents the linear graph. _______________
c. This is a proportional relationship because the graph shows ______________
Options: 2y = x, y = 5x, a constant rate of change, a linear relationship, 2, the points are connected, 5, linear with a y-intercept at (0, 0), 1/2, 1, 1/2y = x, 5y = x, 1/5
Answers
GPT-4o mini
To answer your questions, we need to analyze the given data points.
Given pairs:
- (1, 5)
- (2, 10)
- (3, 15)
- (7, 35)
- (10, 50)
**a. The constant of proportionality (k) is the ratio of y to x.** For example:
- For (1, 5): k = 5/1 = 5
- For (2, 10): k = 10/2 = 5
- For (3, 15): k = 15/3 = 5
- For (7, 35): k = 35/7 = 5
- For (10, 50): k = 50/10 = 5
Thus, the constant of proportionality is **5**.
**b. The equation that represents the linear graph can be written using the formula y = kx, where k is the constant of proportionality found earlier. Here, k = 5. Therefore:**
The equation is: **y = 5x**.
**c. This is a proportional relationship because the graph shows a constant rate of change,** which can also be described as linear with a y-intercept at (0, 0) and all points lie along a straight line that passes through the origin.
So, the completed statements will be:
a. The constant of proportionality is **5**.
b. Write an equation that represents the linear graph: **y = 5x**.
c. This is a proportional relationship because the graph shows **a constant rate of change** (or you could also say **linear with a y-intercept at (0, 0)**).
Given pairs:
- (1, 5)
- (2, 10)
- (3, 15)
- (7, 35)
- (10, 50)
**a. The constant of proportionality (k) is the ratio of y to x.** For example:
- For (1, 5): k = 5/1 = 5
- For (2, 10): k = 10/2 = 5
- For (3, 15): k = 15/3 = 5
- For (7, 35): k = 35/7 = 5
- For (10, 50): k = 50/10 = 5
Thus, the constant of proportionality is **5**.
**b. The equation that represents the linear graph can be written using the formula y = kx, where k is the constant of proportionality found earlier. Here, k = 5. Therefore:**
The equation is: **y = 5x**.
**c. This is a proportional relationship because the graph shows a constant rate of change,** which can also be described as linear with a y-intercept at (0, 0) and all points lie along a straight line that passes through the origin.
So, the completed statements will be:
a. The constant of proportionality is **5**.
b. Write an equation that represents the linear graph: **y = 5x**.
c. This is a proportional relationship because the graph shows **a constant rate of change** (or you could also say **linear with a y-intercept at (0, 0)**).