The document discusses equations of lines. It introduces the linear equation y = 2x - 1 and shows how to graph it by substituting values for x and finding the corresponding y-values. This forms the line's points (ordered pairs). It explains that a linear equation can be written in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. It provides examples of writing equations from their graphs in slope-intercept form and graphing lines from equations written in this form by using the slope and y-intercept. Finally, it gives examples of writing equations of lines parallel or perpendicular to given lines that pass through a given point.

1. Equations of LinesEquations of Lines
You will learn to write and graph equations of lines.
The equation y = 2x – 1 is called a _____________ because its graph is
a straight line.
linear equation
We can substitute different values for x in the graph to find corresponding
values for y.
0
y
0 x
81 3 5 7
-1-1
2
4
6
8
-1 4 8
1
5
-1 6
3
2
7
8
x y = 2x -1 y
1
2
3
y = 2(1) -1 1
3
5
y = 2(2) -1
y = 2(3) -1
(1, 1)
(2, 3)
(3, 5)
There are many more points whose ordered
pairs are solutions of y = 2x – 1.
These points also lie on the line.

2. Equations of LinesEquations of Lines
0
y
0 x
5-2 1 3 5
5
-2
1
3
5
-3 2
-3
-1
4
-1
-3
-3
2
4
y = 2x – 1
Look at the graph of y = 2x – 1 .
The y – value of the point where the line crosses the y-axis is ___.- 1
This value is called the ____________ of the line.y - intercept
(0, -1)
Most linear equations can be written in the form __________.y = mx + b
This form is called the ___________________.slope – intercept form
y = mx + b
slope y - intercept

3. Equations of LinesEquations of Lines
Slope –
Intercept
Form
An equation of the line having slope m and y-intercept b is
y = mx + b

4. Equations of LinesEquations of Lines
1) Rewrite the equation in slope – intercept form by solving for y.
2x – 3 y = 18
2) Graph 2x + y = 3 using the slope and y – intercept.
y = –2x + 3
0
y
0 x
5-2 1 3 5
5
-2
1
3
5
-3 2
-3
-1
4
-1
-3
-3
2
4
1) Identify and graph the y-intercept.
2) Follow the slope a second point on
the line.
(0, 3)
(1, 1)
3) Draw the line between the two
points.

5. Equations of LinesEquations of Lines
1) Write an equation of the line parallel to the graph of y = 2x – 5 that
passes through the point (3, 7).
2) Write an equation of the line parallel to the graph of 3x + y = 6 that
passes through the point (1, 4).
3) Write an equation of the line perpendicualr to the graph of
that passes through the point ( - 3, 8).
5
4
1
+= xy
y = 2x + 1
y = -3x + 7
y = -4x -4