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.
NOTES
Slope-Intercept Form of a linear equation:
y = mx + b
Where “m” is the slope, and “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. Graph the y-intercept
a. Determine what number is in the “b” position
b. The coordinates of the y-intercept are (0,b)
3. Use the slope to count from the y-intercept to get to another point
a. Make the slope a fraction if it’s not already so
b. ****Start at the y-intercept!!
c. The numerator tells you to go up/down
d. The denominator tells you to go left/right
4. Connect the two points with a straight line and use arrows
Graphing Linear Equations Using Slope and
Intercepts
EXAMPLES
1) Graph this equation: y = -3x – 2
1) already in slope-intercept form
2) y-intercept is (0, -2)
y
5
3) slope is -3
4
3
2
1
-5
-4
-3
-2
-1
1
2
3
4
5
x
-1
-2
-3
-4
-5
2) Graph this equation: 3y = 2x + 6
1) put in slope intercept form
3y = 2x + 6
3
3
y
2) y-intercept is ______
5
y = _________
4
3) slope is _____
3
2
1
-5
-4
-3
-2
-1
1
-1
-2
-3
-4
-5
2
3
4
5
x
Graphing Linear Equations Using Slope and
Intercepts
3) Graph this equation: 3x + 2y = -8
1) put in slope-intercept form
3x + 2y = -8
2) y-intercept is ______
y
5
3) slope is _____
4
3
2
1
-5
-4
-3
-2
-1
1
2
3
4
5
x
-1
-2
-3
-4
-5
4) Graph this equation: -8 = 4y – x
-8 = 4y – x
1) put in slope intercept form
y
2) y-intercept is ______
5
4
3) slope is _____
3
2
1
-5
-4
-3
-2
-1
1
-1
-2
-3
-4
-5
2
3
4
5
x
Graphing Linear Equations Using Slope and
Intercepts
MORE NOTES
To solve an equation for the X-intercept:
1. Replace the Y with a “0”
2. Solve the equation for X
3. Write the X-intercept as an ordered pair… (x, 0)
To solve an equation for the Y-intercept:
1. Replace the X with a “0”
2. Solve the equation for Y
3. Write the Y-intercept as an ordered pair… (0, y)
MORE EXAMPLES
1)
3y – 2x = 12
Finding the x-intercept
Finding 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)
2)
2x + 4y = -2
Finding the x-intercept
Finding 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
3)
3x – 4y = -6
4)
20 – 5y = 10x
5)
y = 3x + 5
6)
10y = -2x + 15
GRAPHING OPTION!!
You already have two options to graph linear equations…
1. Make a T-table of values and plot those ordered pairs on the graph
2. Rewrite the equation in slope intercept form (y = mx + b) and plot the yintercept first, then use the slope to count to the next point
NOW!! You have #3!!
3. Find the X and Y intercepts and plot those points on the graph
Show all 3 methods to graph:
4y + 2x = -8