Question

the slope is 6. (simplify your answer.) which graph represents this relationship? a. b. c.

Explanation:

Step1: Recall slope - definition

The slope $m$ of a line is given by $m=\frac{\Delta y}{\Delta x}$. A slope of $6$ means for every increase of $1$ in the $x -$ value, the $y -$ value increases by $6$.

Step2: Analyze option A

In option A, when $x$ increases from $0$ to $30$, $y$ increases from $0$ to $30$. The slope $m=\frac{30 - 0}{30 - 0}=1$.

Step3: Analyze option B

In option B, when $x$ increases from $0$ to $30$, $y$ increases from $0$ to $30$. The slope $m=\frac{30 - 0}{30 - 0}=1$.

Step4: Analyze option C

In option C, when $x$ increases by $5$, $y$ increases by $30$. The slope $m=\frac{30}{5}=6$.

Answer:

C.