1.3
Linear Equations in Two Variables
Slope of a Line
rise y2 ! y1
m=
=
run x2 ! x1
Find the slope of the lines passing through…
a. (-2,0) and (3,1)
b. (-1,2) and (2,2)
c. (4,-3) and (4,5)
1
Ans. ,0, !
5
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
Summary of Equations of Lines
1.
2.
3.
4.
5.
General Form
Vertical Line
Horizontal Line
Slope-intercept
Point-slope form
Ax + By + C = 0
x=a
y=b
y = mx + b
y – y1 = m(x – x1)
Parallel lines have slopes that are Equal.
Perpendicular lines have negative reciprocal
slopes.
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
2
y + 1 = (x ! 2 )
3
2
4
y +1 = x !
3
3
Mult. each term
by 3.
3y + 3 = 2x - 4
0 = 2x – 3y – 7 or
2
7
y = x!
3
3
b.)
What is our slope?
3
m=!
2
Use point-slope form to start. Then put in
general form.
3
y + 1 = ! (x ! 2 )
2
3
y +1 = ! x + 3
2
2 y + 2 = !3 x + 6
3x + 2 y ! 4 = 0
Dist.
Mult. By 2