Slope formula

m

=

y2 - y1 x2 - x1

where (x1, y1) and (x2, y2) are two points on the line

Slope-intercept form

y = mx + b   where m is the slope

Point-slope form

y - y₁ = m (x - x₁ )   where m is the slope and (x₁ , y₁) is a point on the line

Example 1: Slope and point

Solve. Answer using slope-interecept form.
In slope-intercept form, write the equation of a line that goes through point (-2, 1) with slope 5.
Equation:

y	=	mx + b	1.	Take what you know and plug it into the slope-intercept formula.
1	=	5(-2) + b		m = 5 and (x, y) = (-2, 1)
1	=	-10 + b	2.	Solve for b
11	=	b
y	=	5x + 11	3.	Plug m and b into the slope-intercept formula for the answer

The answer is

Example 2: Two points

Solve. Answer using slope-interecept form.
In slope-intercept form, write the equation of a line that goes through point (0, -2) and (2, -5).
Equation:

1. Calculate the slope using (x₁, y₁) = (0, -2) and (x₂, y₂) = (2, -5)

m

=

y2 - y1 x2 - x1

=

-5 - (-2) 2 - 0

=

-3 2

2. Take what you know and plug it into the point-slope formula

y - y1	=	m	(x - x1 )
y - (-2)	=	-3 2	(x - 0)

3. Put the equation in slope-intercept form by solving for y

y + 2	=	-3 2	x
y	=	-3 2	x - 2

The answer is