Question

try this one!
what is the equation of the line that passes through the points (6, 5) and (7, 7)?

1. find the slope of the line. \t\t\tm =

1. find the y - intercept of the line. \t\t\tb =

1. write the equation of the line in slope - intercept form

Explanation:

Part 1: Find the slope of the line

Step1: Recall slope formula

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Here, \( (x_1,y_1)=(6,5) \) and \( (x_2,y_2)=(7,7) \).
So, \( m=\frac{7 - 5}{7 - 6}=\frac{2}{1} = 2 \).

Step1: Use 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. We know that \( m = 2 \), and we can use one of the points, say \( (6,5) \), to find \( b \).
Substitute \( x = 6 \), \( y = 5 \) and \( m = 2 \) into \( y=mx + b \):
\( 5=2\times6 + b \)

Step2: Solve for \( b \)

\( 5 = 12 + b \)
Subtract 12 from both sides: \( b=5 - 12=- 7 \)

Step1: Recall slope - intercept form

The slope - intercept form is \( y=mx + b \). We know that \( m = 2 \) and \( b=-7 \).

Step2: Substitute \( m \) and \( b \) into the formula

Substitute \( m = 2 \) and \( b=-7 \) into \( y=mx + b \), we get \( y = 2x-7 \)

Answer:

\( m = 2 \)

Part 2: Find the y - intercept of the line