graphing linear equations
DESCRIPTION
Graphing Linear Equations. In Slope-Intercept Form. In order to graph using point plotting, you will need to create a table. You will need to choose at least 3 numbers for x and “plug” them into the equation to find corresponding y values. Plot the points. For Example: Graph y = 2x - 1. - PowerPoint PPT PresentationTRANSCRIPT
Graphing Linear Equations
In Slope-Intercept Form
In order to graph using point plotting, you will need to create a table.
You will need to choose at least 3 numbers for x and “plug” them into the equation to find corresponding y values.
For Example:Graph y = 2x - 1
x yChoose x values
“plug” x into the equation
Plot the points
-1 2(-1)-1=-30 2(0)-1 = -11 2(1)-1 = 1
Graph using point plotting321
xy
x y
-2
0
2
21
21
21
(-2) + 3 = 2
(0) + 3 = 3
(2) + 3 = 4
y 2x 1y x 4
y 32
x 2
These equations are all in Slope-Intercept Form:
Notice that these equations are all solved for y.
Just by looking at an equation in this form, we can draw the line (no tables).
•The constant is the y-intercept. •The coefficient is the slope.
y 2x 1
y x 4
y 32
x 2
Constant = 1, y-intercept = 1.
Coefficient = 2, slope = 2.
Constant = -4, y-intercept = -4.
Coefficient = -1, slope = -1.
Constant = -2, y-intercept = -2.
Coefficient = 3/2, slope = 3/2.
The formula for Slope-Intercept Form is:
y mx b;• ‘b’ is the y-intercept. • ‘m’ is the slope.
On the next three slides we will graph the three equations:
y 2x 1, y x 4, y 32
x 2
using their y-intercepts and slopes.
y 2x 11) Plot the y-intercept as a point on the y-axis. The constant, b = 1, so the y-intercept = 1.
2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = 2, so the slope = 2/1.
up 2
right 1 up 2
right 1
1) Plot the y-intercept as a point on the y-axis. The constant, b = -4, so the y-intercept = -4.
2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = -1, so the slope = -1/1.
right 1down 1
right 1
y x 4
down 1
1) Plot the y-intercept as a point on the y-axis. The constant, b = -2, so the y-intercept = -2.
2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = 3/2, so the slope = 3/2.
right 2
up 3
y 32
x 2
right 2
up 3
Sometimes we must solve the equation for y before we can graph it.
2x y 3
2x y ( 2x) ( 2x) 3
y 2x 3
The constant, b = 3 is the y-intercept.The coefficient, m = -2 is the slope.
1) Plot the y-intercept as a point on the y-axis. The constant, b = 3, so the y-intercept = 3.
2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = -2, so the slope = -2/1.
right 1down 2
right 1
down 2
y 2x 3
Important!!!This is one of the big concepts in
Algebra. You need to thoroughly understand this!
Slope – Intercept Formy = mx + b
m represents the slopeb represents the y-intercept
Graphing Using the Slope-Intercept Form
To graph a linear equation, you will need to find the slope and the y-intercept for the equation.
Remember: y = mx + b
slope Y-intercept (the point where the graph crosses the y-axis)
Graph 132
xy Slope =
Y-intercept =
32
1
1. Plot the y-intercept
2. Use the slope to find the next point
Slope = “rise over run”
Graph 2x + 5y = 10 using the slope-intercept form: (put the equation in slope-intercept form first)
2x + 5y = 10
5y = 10 – 2x
y = 2 – 2/5 x
slope = -2/5y – intercept = 2
A negative slope means you will go down then right from the y-intercept