3.5 Write and Graph Equations of Lines

3.5 Write and Graph Equations of Lines
Objectives:
1. To graph and write
equations of lines
2. To write the
equation of a line
that is parallel or
perpendicular to a
given line
Assignment:
• P. 184-6: 4-44
multiples of 4, 30, 33,
53-59, 67, 68
• Challenge Problems
Objective 1a
You will be able
to graph the
equation of a line
Exercise 1
Line k passes through
(0, 3) and (5, 2).
Graph the line
perpendicular to k
that passes through
point (1, 2).
Intercepts
The 𝒙-intercept of
a graph is where it
intersects the 𝑥axis.
6
4
𝑎, 0
y-intercept
2
0, 𝑏
-5
The 𝒚-intercept of
a graph is where it
intersects the 𝑦axis.
x-intercept
5
-2
Investigation 1
Use the Geometer’s
Sketchpad Activity
“Equations of
Lines” to complete
the Slope-Intercept
Form of a Line.
Slope-Intercept
Slope-Intercept Form of a Line:
If the graph of a line has slope m and a
y-intercept of (0, b), then the equation of
the line can be written in the form
y = mx + b.
Equation of a Horizontal
Line
Equation of a Vertical
Line
𝑦=𝑏
(where 𝑏 is the 𝑦-intercept)
𝑥=𝑎
(where 𝑎 is the 𝑥-intercept)
Exercise 2
Graph the equation:
1
y  x3
2
Slope-Intercept
To graph an equation in slope-intercept form:
Plot
2.
0, 𝑏
Solve
1.
for 𝑦
Draw
4.
line
Use 𝑚
to plot
3.
more
points
Exercise 2
Graph the equation:
2 x  3 y  10
Standard Form
Standard Form of a Line
The standard form of a linear
equation is 𝐴𝑥 + 𝐵𝑦 = 𝐶, where 𝐴
and 𝐵 are not both zero.
Generally taken to be integers
Standard Form
To graph an equation in standard form:
1. = 0
Let 𝑥
2. = 0
Let 𝑦
Solve for 𝑦
Solve for 𝑥
This is the
𝑦intercept
This is the
𝑥-intercept
3. line
Draw
Exercise 3
Without your graphing calculator, graph each
of the following:
1. y = −x + 2
2. y = (2/5)x + 4
3. f (x) = 1 – 3x
4. 8y = −2x + 20
Exercise 4
Graph each of the following:
1. x = 1
2. y = −4
Exercise 5
A line has a slope of −3 and a y-intercept of
(0, 5). Write the equation of the line.
Exercise 7
A line has a slope of ½ and contains the
point (8, −9). Write the equation of the line.
Point-Slope Form
Given the slope and
a point on a line,
you could easily
find the equation
using the slopeintercept form.
Alternatively, you
could use the
point-slope form of
a line.
Point-Slope Form of a Line
A line through (𝑥1, 𝑦1)
with slope m can be
written in the form
𝑦– 𝑦1 = 𝑚(𝑥– 𝑥1).
Exercise 8
Find the equation of the line that contains the
points (−2, 5) and (1, 2).
Exercise 9
Write the equation of the line shown in the
graph.
objective 2a
You will be able to write the equation of a line
that is parallel to a given line
objective 2b
You will be able to write the equation of a line
that is perpendicular to a given line
Exercise 10
Write an equation of the line that passes
through the point (−2, 1) and is:
1. Parallel to the line y = −3x + 1
2. Perpendicular to the line y = −3x + 1
Exercise 11
Find the equation of the perpendicular
bisector of the segment with endpoints
(-4, 3) and (8, -1).
3.5 Write and Graph Equations of Lines
Objectives:
1. To graph and write
equations of lines
2. To write the
equation of a line
that is parallel or
perpendicular to a
given line
Assignment:
• P. 184-6: 4-44
multiples of 4, 30, 33,
53-59, 67, 68
• Challenge Problems