Question

coordinate into the equation for x and the y-coordinate into the equation for y. 13/24 step 4: solve the resulting equation for b. step 5: write the final slope-intercept form of the line by substituting the m and b numbers back into the equation, y = mx + b. what is the equation of the line that passes through the points (-4, -5) and (-5, -7)? 1. find the slope of the line. m = 2. find the y-intercept of the line. b = 3. write the equation of the line in slope-intercept form.

Explanation:

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, \( (x_1, y_1)=(-4, -5) \) and \( (x_2, y_2)=(-5, -7) \).

Step2: Substitute values into formula

Substitute \( x_1=-4,y_1 = - 5,x_2=-5,y_2=-7 \) into the formula:
\( m=\frac{-7-(-5)}{-5 - (-4)}=\frac{-7 + 5}{-5 + 4}=\frac{-2}{-1}=2 \)

Step1: Use slope - intercept form

The slope - intercept form of a line is \( y=mx + b \). We know \( m = 2 \), and we can use one of the points (let's use \( (-4,-5) \)) to find \( b \).
Substitute \( x=-4,y = - 5 \) and \( m = 2 \) into \( y=mx + b \):
\( -5=2\times(-4)+b \)

Step2: Solve for \( b \)

Simplify the right - hand side: \( -5=-8 + b \)
Add 8 to both sides of the equation: \( b=-5 + 8=3 \)

Step1: Recall slope - intercept form

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

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

We know \( m = 2 \) and \( b = 3 \), so substitute these values into the equation: \( y=2x+3 \)

Answer:

\( m = 2 \)

2. Find the y - intercept of the line.