Transcript Standard Form

Objective: to graph linear equations
that are in standard form
Do-Now:
1. Check homework with answer key.
2. Grab a “More Work Graphing Linear
Functions” Handout; Complete this
independently
3. Grab a sheet of graph paper – you will
need this for today’s notes
Graphing Linear Equations
In Standard Form
Ax + By = C
Today we will use
The Standard
Form
of the equation to graph the line.
The formula for Standard Form is:
Ax + By = C
To find where the line crosses each axis,
let the other value be zero.
We can find 3
things just by
looking at the
formula:
• If y is zero, we have Ax = C
C
is the x-intercept.
A
• If x is zero, we have By = C
C
is the y-intercept.
B
A
• −—
is
the
slope.
B
Using the x-intercept and/or y-intercept as a starting
point, you can use the slope to graph more points on
the line of the equation.
These equations are all in
Standard Form:
2x – y = -1
x + y = -4
3x – 2y = 4
Notice that these equations are all in the
form Ax + By = C.
2x – y = -1
1) Find the x-intercept:
-1 ÷ 2 = -1/2
right 1
right 1 up 2
up 2
2) Find the y-intercept:
-1 ÷ -1 = 1
3) Plot the y-intercept.
4) Find the slope:
-A/B
− 2/-1 = 2
5) Plot more points using
the slope.
x + y = -4
1) Find the x-intercept:
-4 ÷ 1 = -4
2) Find the y-intercept:
-4 ÷ 1 = -4
3) Plot the x and yintercepts.
left 1
up 1
down 1
right 1
4) Find the slope:
-a/b
− 1/1 = -1
5) Plot more points using
the slope.
A graph with only one letter (x or y)
only crosses that axis at that point.
x = -3
ONLY crosses the
x-axis…
at -3
y=5
ONLY crosses the
y-axis…
at 5
SUMMARY
The formula for Standard Form is:
Ax + By = C
• If y=0, C ÷ A gives the
x-intercept
• If x=0, C ÷ B gives the
y-intercept
A
• − — is the
B
slope
Using the x-intercept and/or y-intercept as
a starting point, you can use the slope to
graph the line of the equation.
Quick Info on the Coefficient!
• A shouldn't be negative
• A and B shouldn't both be zero
• A, B and C should be integers
You must clear any fractions you see!
Quick Application
A hiker is hiking down a
canyon toward the canyon
floor. Her height above the
canyon floor as a function of
time is shown in the graph
below.
a. Interpret the meaning of the
y-intercept
b. Interpret the meaning of the
x-intercept
What are the x- and y-intercepts?
The table below shows the distance
remaining in a bus trip from Houston to
Dallas as a function of time.
What does the x-intercept represent?
The table below shows the distance
remaining in a bus trip from Houston to
Dallas as a function of time.
What does the y-intercept represent?
Write equation in slope-intercept form

Write the equation that describes each
line in the slope-intercept form
slope = 3, y-intercept = (0, –2)
y = 3x – 2
What is the easiest way to graph an
equation in Standard Form?
Using the x-intercept and the y-intercept
Take the equation from standard form
to slope-intercept form
6x + 2y = 10
y = –3x + 5
Write an equation that describes each
line the slope-intercept form.
Slope = –2, (2, 1) is on the line
y = –2x + 5
Write the equation that describes each
line in the slope-intercept form.

y=
Write an equation that describes each
line the slope-intercept form.
(0, 4) and (–7, 2) are on the line
Slope-Intercept
The cost to take a taxi from the airport is a linear
function of the distance driven. The cost for 5, 10, and
20 miles are shown in the table. Write an equation in
slope-intercept form that represents the function.
y = 1.6x + 6
Slope-Intercept
The following equation shows the cost to take a taxi
from the airport is a linear function of the distance
driven. Interpret the meaning of the slope in context
to the situation.
y = 1.6x + 6
Slope-Intercept
The following equation shows the cost to take a taxi
from the airport is a linear function of the distance
driven. Interpret the meaning of the y-intercept in
context to the situation.
y = 1.6x + 6
Interpret the meaning of the y-intercept.
Interpret the meaning of the x-intercept.
Write the equation that describes each
line in the slope-intercept form.

Take the equation from standard form
to slope-intercept form
x–y=6
y=x–6
Write an equation for the line that
passes through the coordinates in
all 3 forms: (-6, -2) and ( -10, 14)
Point-Slope Form
b. Slope-Intercept Form
c. Standard Form
a.
Closure: Identify the form of each
linear equation.
• You may work with a partner or
independently on this
Homework: Practice 6.3
• Only do the multiples of 4
• You will need graph paper
6.1-6.4 Mixed Practice Day
Do-Now:
1. Check homework with answer key
2. Grab the “3 Forms of a Line” handout
Homework questions?
6.1-6.4 Quiz