Question

which lines in the graph have a slope greater than 1 but less than 2?
line 1
line 2
line 3
line 4
line 5

Explanation:

Step1: Recall slope formula

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For lines passing through the origin $(0,0)$ and another point $(x,y)$, the slope is $m = \frac{y}{x}$.

Step2: Calculate slopes of each line

For line 1: It passes through $(0,0)$ and $(1,6)$. So $m_1=\frac{6 - 0}{1 - 0}=6$. Since $1<6<7$.
For line 2: It passes through $(0,0)$ and $(2,6)$. So $m_2=\frac{6 - 0}{2 - 0}=3$. Since $1<3<7$.
For line 3: It passes through $(0,0)$ and $(3,6)$. So $m_3=\frac{6 - 0}{3 - 0}=2$. Since $1<2<7$.
For line 4: It passes through $(0,0)$ and $(4,6)$. So $m_4=\frac{6 - 0}{4 - 0}=\frac{3}{2}=1.5$. Since $1<1.5<7$.
For line 5: It passes through $(0,0)$ and $(5,6)$. So $m_5=\frac{6 - 0}{5 - 0}=\frac{6}{5}=1.2$. Since $1<1.2<7$. All of line 1 - line 5 have slopes greater than 1 and less than 7.

Answer:

A. line 1, B. line 2, C. line 3