Download 2-4 More about linear equations

Write an equation of a line by using the slope and a
point on the line.
Point-Slope Form

Uses one point, (x1, y1) on a line to
create an equation
Writing an Equation
A line passes through (-3, 6) and has a
slope of -5.
 𝑦 − 𝑦1 = m(𝑥 − 𝑥1 )
 Plug in the slope an d point
 𝑦 − 6 = -5(𝑥 − (−3))
 y – 6 = -5(x + 3)

Graphing

y–1=
2
(x
3
– 2)
2
3

We know the slope is

And it passes through the point (2, 1)
Standard Form of a Linear
Equation

So far we have learned how to write
linear equations in slope-intercept form
and point-slope form.

Standard form is written Ax + By = C
where A, B, and C are real numbers
Intercepts

The x-intercept is the x-coordinate of a
point where a graph crosses the x-axis.
 Found where the y-value is 0
Find x and y intercepts of the graph of
3x + 4y = 24
 Sub 0 for y to find x-intercept

 X =8

Sub 0 for x to find y-intercept
Y=6
Graphing Using Intercepts
What is the graph of x – 2y = -2?
 Find intercepts

 X = -2
Y=1

Write as ordered pairs
 (-2, 0)
 (0, 1)

Plot the ordered pairs
Horizontal and Vertical Lines
x=3
 Write in standard form: 1x + 0y = 3

y=3
 Standard form: 0x + 1y = 3

Transforming to Standard Form
3
− 𝑥
7
+ 5 in standard form

What is y =

Get rid of fractions by multiplying by 7

7y =
3
7(− 𝑥
7
+ 5)
Distribute: 7y = -3x + 35
 Add 3x: 7y + 3x = 35
 Done!
 These equations, though they look
different, are equivalent.

Parallel Lines

Lines in the same plane that never
intersect.
Nonvertical lines are parallel if they have
the same slope and different y-intercepts.
 Vertical lines are parallel if they have
different x-intercepts.
 Ex:

 Same slope, different y-intercept
Perpendicular lines

Lines that intersect to form right angles

Two nonvertical lines are perpendicular if
the product of their slopes is -1.
 The slope is the opposite reciprocal.
 Ex: the opposite reciprocal of
3
−
4
4
3
is since their
product is -1.

A vertical line and a horizontal line are
always perpendicular.