2.2 Linear Equations
Objective:

SW graph linear equations

SW write the equations of lines
Warmup
________________________________________________________________________
List some things that come to mind when you hear the word SLOPE.
Possible Graphs of Lines
1.
2.
3.
4.
Horizontal lines have a slope
of __________.
Vertical Lines have an
__________________ slope.
Finding Slope
Slope formula:
Find the slope of the lines going through the two given points.
1. (-2, 3) (-4, 4)
3. (5, 7) (5, -3)
2.
(7, 5) (-3, 5)
Another method for finding slope – helpful with graphs
4.
5.
Writing Linear Equations
Given certain information, you will need to write the linear function in 3 ways:
I.
SLOPE-INTERCEPT FORM:
To do this, you must know the _______________ (
Write the linear equation in slope-intercept form.
1. Slope = -3 y-intercept = 8
2. m = 2 and goes through point (1, -3)
3.
going through points (2, 0) and (4, -3)
) and the ______________ (
).
II.
POINT – SLOPE FORM:
To do this, you must know the _______________ (
) and a __________________ .
Write the linear equation in point-slope form.
1.
Slope is 2, going through point (4, - 5)
2.
Going through points (1, 5) and (4, -1)
III.
STANDARD FORM:
Rules:
Write the linear equation in standard form. You can start off using any of the two methods and
then change it into standard form.
1.
slope = 4 and y – intercept = -5
2. Goes thru points (6, - 2) and (1, 8)
Rearrange to put into standard form.
3.
-2x + 10y = 7
5.
12x = 8y – 6
4. 9 x  3 y  1
4
GRAPHING TIME!!!
Linear Function –
A solution to any linear function is any ordered pair (x, y) on its line.
Is (1, 6) or (2, 0) a solution to y = -2x + 4?
Methods of graphing for linear functions:
Table of values
y = -2x + 4
Parallel and Perpendicular Lines:
Slope-intercept form
y = -2x + 4
x and y-intercepts
y = -2x + 4
Are these lines parallel or perpendicular?
Ex. 1
6y = 2x + 18
3y - x = 7
Ex. 2
4x + y = 7
-x + 4y = 16
Write the linear function in slope-intercept form.
1. Write an equation of the line that is parallel to y = 2x + 5 and goes through (3, 2).
2. Write an equation of the line that is perpendicular to y = 2x + 5 and goes through (4, -1).
Horizontal Line:
Vertical Line: