To graph the linear relationship between the number of stuffed animals (x) and the number of action figures (y), you can start by plotting the two given points:
- (20, 15) - This point represents when 20 stuffed animals are displayed, and 15 action figures are also displayed.
- (60, 45) - This point represents when 60 stuffed animals are displayed, and 45 action figures are also displayed.
To check if the relationship is proportional, we can determine the slope of the line formed by these two points. The slope (m) can be calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points (20, 15) and (60, 45):
- \(x_1 = 20, y_1 = 15\)
- \(x_2 = 60, y_2 = 45\)
Calculating the slope:
\[ m = \frac{45 - 15}{60 - 20} = \frac{30}{40} = \frac{3}{4} \]
Now, since both the number of stuffed animals and the number of action figures can be expressed in a linear equation of the form \(y = mx + b\), where \(b\) is the y-intercept. A proportional relationship has a slope with no y-intercept (meaning it passes through the origin, (0,0)).
To find the y-intercept, we can substitute one of the existing points into the equation of the line. Let's use the point (20, 15):
\[ 15 = \frac{3}{4}(20) + b \] \[ 15 = 15 + b \] \[ b = 0 \]
Since we found that the y-intercept \(b = 0\), the relationship is indeed proportional.
Now, mark the two points on your graph and draw a line that connects these points. Then, place a point or label to indicate that the relationship is proportional. The line should also pass through the origin (0,0).
Let me know if you need any more information about this topic!
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