Algebra II
Linear Equations
Name:_______________
1.
How do you know when an equation is linear?
2.
Is the point (-2, 2) a solution to the equation y  3 x  4 ? Prove it (algebraically).
How do you find the slope of a line through two points
HINT: See page 64 of your textbook.
and
?
Finding Equations of Lines
You must learn a variety of techniques and use an appropriate method, not your favorite method.
Certain given information in a problem should lead you to using certain methods.
I.
Three Methods for writing the equation of a line (see examples below)…
Slope Intercept Form
Point Slope formula
y  mx  b
y  y1  m( x  x1 )
m = slope =
m = slope =
b = y-intercept (0, b)


When given slope and a point,
substitute slope for m and point
in for x and y. Solve for
the y-intercept b, and then write
equation in y  mx  b
When given 2 points, find slope
m. Then, pick one point and use
above method to find equation
Ex: Find the slope intercept equation
of the line with slope of
through
= given point on the line


When given slope and a point,
simply substitute the point in
for and .
When given 2 points, find the
slope and then pick one point to
substitute for
and .
Ex: Find the point –slope equation of
the line with slope of 3 through the
point (-1, 4).
Standard Form
A, B, and C are integers


When graphing from standard
form, find the x-and yintercepts by substituting “0”
for x and solving for y and then
substituting “0” for y and
solving for x.
To write and equation in
standard form from one of the
other linear forms, use algebra
to get x and y on the left side
and a number “C” on the right.
Ex: Graph 2x – 3y = 6 using intercepts.
the point (2, -6).
Ex: Find the point-slope equation of
the line through (9, 2) and (-3, 5).
Ex: Find the slope intercept equation
of the line through (-1, 0) and (-6, 5)
Ex: Write y – 2 =-1(x - 5) in standard
form.
Find the equation of the line in the form y  mx  b .
3.
m  7 through the point (-2, 19)
4.
(-2, 7) and (5, -7)
Find the equation of the line in the form y  y1  m( x  x1 ) .
2
through the point (1, 5)
3
5.
m
6.
(-4, 2) and (7, 4)
II. Special Cases
Horizontal Lines


Vertical Lines
Horizontal (
) lines have a slope
of 0, because the “rise” is 0 and the “run”
is infinite.
The equation of a horizontal line is y = b,
where b is the y-intercept


Vertical ( ) lines have an undefined
slope, because the “rise” is infinite and
the “run” is 0. Since m =
, and we
cannot divide by 0, slope is undefined.
The equation of a vertical line is x = c,
where c is the x-intercept
Look at page 66-67 in your book to help you with #7-10.
7.
8.
a
, then m2  _____
b
a
With Perpendicular lines the slopes __________________________. So, If m  , then m2  _____
b
With Parallel lines the slopes are _________________________. So, if m1 
9.
Find the equation of line parallel to y  2 x  1 through the point (14, 2).
10.
Find the equation of line perpendicular to y  2 x  1 through the point (14, 2).
Write an equation for each line (you choose the form that makes sense).
11.
through (1, 3) and parallel to y = 2x + 1
12.
through (2, 2) and perpendicular to y =  x + 2
13.
through (3, 4) and vertical
14.
through (4, 1) and horizontal
15.
y-intercept of 2.1, x-intercept of 3.5
3
5
Write in point-slope form the equation of the line through each pair of points.
16.
(3, 2) and (1, 6)
Write in standard form an equation of the line with the given slope through the given point.
17.
slope = 4;(2, 2)
18.
slope = 0; (3, 4)
Graph each line.
19.
3x  4y = 12
20.
y = 2
Find the slope of each line.
22.
23.
21.
x=5