Question

build your skills

1. calculate the slope of the two lines on the graph. which is steeper?
2. calculate the slopes of the two lines on the graph.

Explanation:

Step1: Recall slope formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.

Step2: For the first - graph

For line $\ell_1$ in the first graph, assume two points $(0,0)$ and $(10,7)$. Then $m_1=\frac{7 - 0}{10 - 0}=\frac{7}{10}=0.7$. For line $\ell_2$ in the first graph, assume two points $(0,0)$ and $(5,8)$. Then $m_2=\frac{8 - 0}{5 - 0}=\frac{8}{5}=1.6$. Since $1.6>0.7$, $\ell_2$ is steeper.

Step3: For the second - graph

For line $\ell_1$ in the second graph, assume two points $(3,7)$ and $(10,7)$. Then $m_3=\frac{7 - 7}{10 - 3}=0$. For line $\ell_2$ in the second graph, assume two points $(5,3)$ and $(5,10)$. Then $m_4=\frac{10 - 3}{5 - 5}$, the denominator is 0, so the slope of $\ell_2$ is undefined. A vertical line (with undefined slope) is steeper than a horizontal line (with slope 0).

Answer:

In the first graph, $\ell_2$ is steeper. In the second graph, $\ell_2$ is steeper.