Download graphing linear equations

Graphing Linear Equations Using Slope and
Intercepts
Objectives:
…to write an equation in slope-intercept form
...to graph a linear equation using slope and the y-intercept
...to find the x-intercept and y-intercept of a linear equation
...to graph a linear equation using intercepts
Assessment Anchor:
8.C.3.1 – Plot and/or identify ordered pairs on a coordinate plane.
8.D.4.1 – Represent relationships with tables or graphs on the coordinate
plane.
Vocabulary alert!!
Y-INTERCEPT (of a line) – the point where the line
intersects the y-axis
NOTES
y = mx + b
“m” is the slope
(slope-intercept form)
“b” is the y-coordinate of the y-intercept
To graph linear equations (using slope-intercept form):
1. Rearrange the equation so that it is in slope-intercept form
2. Determine the y-intercept and plot that point on the graph.
3. Determine the slope and use it to plot a second point.
a. Make the slope a fraction if it’s not already.
b. Beginning at the y-intercept…use the “rise” number to travel
up or down, use the “run” number to travel left or right.
4. Connect the two points with a straight line and use arrows.
Graphing Linear Equations Using Slope and
Intercepts
EXAMPLES
1)
y = -3x – 2
y = mx + b
y = -3x – 2 (already in form)
y-intercept
(0, -2)
slope
m=
2)
3y = 2x + 6
y-intercept
( , )
slope
m=
3)
3x + 2y = -8
y-intercept
( ,
slope
m=
)
Graphing Linear Equations Using Slope and
Intercepts
Vocabulary alert!!
X-INTERCEPT (of a line) – the point where the line
intersects the x-axis
MORE NOTES and EXAMPLES
To find an X-intercept:
To find a Y-intercept:
A. Replace the “y” with zero
B. Solve the equation for “x”
A. Replace the “x” with zero
B. Solve the equation for “y”
4)
3y – 2x = 12
Find the x-intercept
Find the y-intercept
3(0) – 2x = 12
-2x = 12
-2 -2
x = -6
3y – 2(0) = 12
3y = 12
3 3
y=4
x-intercept: (-6, 0)
y-intercept: (0, 4)
5)
2x + 4y = -2
Find the x-intercept
Find the y-intercept
2x + 4(0) = -2
2x = -2
2 2
x = -1
2(0) + 4y = -2
4y = -2
4 4
y = -½
x-intercept: (-1, 0)
y-intercept: (0, -½)
Graphing Linear Equations Using Slope and
Intercepts
6)
Find the x-intercept
Find the y-intercept
7)
Find the x-intercept
3x – 4y = -6
10y = -2x + 15
Find the y-intercept
“This now means…that there are THREE
methods we can use to graph linear equations.
We can use a T-table, or we can use
slope-intercept form, or we can find the
intercepts!”