Question

lines a, b, and c show proportional relationships. which line has a constant of proportionality between y and x of 1? choose 1 answer: a a b b c c

Explanation:

Step1: Recall the formula for constant of proportionality

For a proportional relationship $y = kx$, $k$ is the constant of proportionality. When $k = 1$, the equation is $y=x$. This means for every value of $x$, the value of $y$ is the same. On a graph, the line $y = x$ has a slope of 1 and passes through the origin $(0,0)$ and points like $(1,1)$, $(2,2)$ etc.

Step2: Analyze the lines

Line $A$ has a steeper slope than 1. For example, if we take a point on line $A$ like $(1, 3)$ (approx - by visual inspection), the ratio $\frac{y}{x}=\frac{3}{1}=3$. Line $C$ has a shallower slope than 1. For example, if we take a point on line $C$ like $(4,1)$ (approx - by visual inspection), the ratio $\frac{y}{x}=\frac{1}{4}=0.25$. Line $B$ passes through points such as $(2,2)$ (by visual inspection). The ratio $\frac{y}{x}=\frac{2}{2} = 1$.

Answer:

B. $B$