Answer/Step-by-step explanation:
7. The graph is a proportional relationship because the line passes through the point of origin, (0, 0). To find the equation the proportional relationship the graph represents, we need to find the unit rate of red paint (y) to white paint (x). The unit rate will represent the constant of proportionality, k. Then substitute the value of k in [tex] y = kx [/tex].
Unit rate or k = y/x
Using the point, (4, 1),
k = [tex] \frac{1}{4} [/tex]
Substitute k = ¼ in [tex] y = kx [/tex]
✅The equation would be:
[tex] y = \frac{1}{4}x [/tex]
8. The graph Franco made is incorrect.
The equation, [tex] y = -x [/tex], shows a negative constant of proportionality of -1. Therefore, the slope of the line descend downwards, from the left to the right. So, the graph Franco made to represent the equation, [tex] y = -x [/tex] is not correct.
9. a. Proportional relationship can be represented as [tex] y = kx [/tex]. To derive an equation that represents the graph, find k, the constant of proportionality between variable y and x.
Using the point, (2, 24), therefore:
k = y/x = 24/2 = 12.
Substitute k = 12 in [tex] y = kx [/tex]
✅The equation would be:
[tex] y = 12x [/tex]
b. We know an equation is represents a proportional relationship, when it is tales the form, [tex] y = kx [/tex]. Where k is the constant of proportionality. Thus, for if you substitute the pair of values given (x, y) into the equation, you would get the same value of k for any pair of value you substitute in the given set of values.
Also, we know a graph represents a proportional relationship when a straight line passes through the point of origin, (0, 0), and has a constant of proportionality or unit rate all through.
