Question

find the slope of each line

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 line 1

Let's take two points on line 1, say $(-8,1)$ and $(6,8)$. Then $m_1=\frac{8 - 1}{6-(-8)}=\frac{7}{14}=\frac{1}{2}$.

Step3: For line 2

Line 2 is a vertical line. For a vertical line, the $x$-coordinates of all points are the same. The slope of a vertical line is undefined since the denominator in the slope - formula $x_2 - x_1 = 0$.

Step4: For line 3

Let's take two points on line 3, say $(-2,-9)$ and $(-1,-2)$. Then $m_3=\frac{-2-(-9)}{-1-(-2)}=\frac{-2 + 9}{-1 + 2}=\frac{7}{1}=7$.

Step5: For line 4

Let's take two points on line 4, say $(0,2)$ and $(6,-7)$. Then $m_4=\frac{-7 - 2}{6-0}=\frac{-9}{6}=-\frac{3}{2}$.

Answer:

Line 1 slope: $\frac{1}{2}$; Line 2 slope: Undefined; Line 3 slope: $7$; Line 4 slope: $-\frac{3}{2}$