1. 1.3 Linear Equations in Two Variables
Slope of a Line
Find the slope of the lines passing through…
(-2,0) and (3,1)
(-1,2) and (2,2)
(4,-3) and (4,5)

2. Point-slope Form of the Equation of a Line
Given a point (x1,y1) and slope m
y – y1 = m(x – x1)
Ex. Find an equation of the line that passes
through the point (1,-2) and has a slope of 3.
y – (-2) = 3(x – 1)
y + 2 = 3(x – 1)
0 = 3x – y - 5

3. Summary of Equations of Lines
General Form Ax + By + C = 0
Vertical Line x = a
Horizontal Line y = b
Slope-intercept y = mx + b
Point-slope form y – y1 = m(x – x1)
Parallel lines have slopes that are Equal.
Perpendicular lines have negative reciprocal
slopes.

4. Ex. Find the equations of the lines that pass
through the point (2,-1) and are a.) parallel to
and b.) perpendicular to the line 2x – 3y = 5.
First, solve for y and find the slope of the line.
a.) m = 2/3
Use point-slope form
Mult. each term
by 3.
3y + 3 = 2x - 4
0 = 2x – 3y – 7 or

5. b.) What is our slope?
Use point-slope form to start. Then put in
general form.
Dist.
Mult. By 2