Question

now you try!
what is the equation of the line that
passes through the points (-5, 3)
and (5, 5)?

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

the line.

1. write the equation of the

line in slope-intercept form.

Explanation:

Part 1: Find the slope of the line

Step1: Recall the slope formula

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify the points

Here, \( (x_1, y_1)=(-5, 3) \) and \( (x_2, y_2)=(5, 5) \).

Step3: Substitute into the formula

\( m=\frac{5 - 3}{5 - (-5)}=\frac{2}{5 + 5}=\frac{2}{10}=\frac{1}{5} \)

Step1: Recall the 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 \( m=\frac{1}{5} \), and we can use one of the points (let's use \( (5, 5) \)) to find \( b \).

Step2: Substitute into the equation

Substitute \( x = 5 \), \( y = 5 \) and \( m=\frac{1}{5} \) into \( y=mx + b \): \( 5=\frac{1}{5}(5)+b \)

Step3: Solve for \( b \)

Simplify the right - hand side: \( \frac{1}{5}(5)=1 \), so the equation becomes \( 5 = 1 + b \). Subtract 1 from both sides: \( b=5 - 1 = 4 \)

Step1: Recall the slope - intercept form

The slope - intercept form is \( y=mx + b \).

Step2: Substitute \( m \) and \( b \)

We know that \( m=\frac{1}{5} \) and \( b = 4 \), so substitute these values into the equation.

Answer:

\( \frac{1}{5} \)

Part 2: Find the y - intercept of the line