Question

fill in the blanks below.
(a) find the slope of the line passing through the points (-7, 4) and (-7, 9).
slope:
(b) find the slope of the line passing through the points (8, 6) and (8, -6).
slope:

Explanation:

Step1: Recall the slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \), provided \( x_2
eq x_1 \). If \( x_1 = x_2 \), the line is vertical and the slope is undefined.

Step2: Solve part (a)

For the points \((-7, 4)\) and \((-7, 9)\), we have \( x_1=-7 \), \( y_1 = 4 \), \( x_2=-7 \), \( y_2 = 9 \).
Since \( x_1=x_2=-7 \), the denominator \( x_2 - x_1=-7-(-7)=0 \). So the slope is undefined.

Step3: Solve part (b)

For the points \((8, 6)\) and \((8, -6)\), we have \( x_1 = 8 \), \( y_1=6 \), \( x_2 = 8 \), \( y_2=-6 \).
Since \( x_1=x_2 = 8 \), the denominator \( x_2 - x_1=8 - 8=0 \). So the slope is undefined.

Answer:

(a) slope: undefined
(b) slope: undefined