Question

find the slope of the line through each pair of points.

1. (6, 4), (-10, 10) 67) (-20, -7), (-14, 17)

write the slope-intercept form of the equation of each line given the slope and y-intercept

1. slope = \\(\frac{5}{2}\\), y-intercept = -5 69) slope = -4, y-intercept = -1

Explanation:

Problem 66:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Let \((x_1,y_1)=(6,4)\) and \((x_2,y_2)=(-10,10)\).

Step2: Substitute values into formula

Substitute \( x_1 = 6,y_1 = 4,x_2=- 10,y_2 = 10 \) into the formula:
\( m=\frac{10 - 4}{-10 - 6}=\frac{6}{-16}=-\frac{3}{8} \)

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Let \((x_1,y_1)=(-20,-7)\) and \((x_2,y_2)=(-14,17)\).

Step2: Substitute values into formula

Substitute \( x_1=-20,y_1 = - 7,x_2=-14,y_2 = 17 \) into the formula:
\( m=\frac{17-(-7)}{-14-(-20)}=\frac{17 + 7}{-14 + 20}=\frac{24}{6} = 4\)

Step1: Recall slope - intercept form

The slope - intercept form of a line is \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept.

Step2: Substitute values

Given \( m=\frac{5}{2}\) and \( b=-5 \), substitute into \( y = mx + b \):
\( y=\frac{5}{2}x-5 \)

Answer:

The slope is \(-\frac{3}{8}\)

Problem 67: