Graphing lines using the equation

• Identify the Y-intercept (b) and graph it on the y-axis with a point.

• Identify what the slope is (m). Remember slope is rise over run.

• From the point on the y-axis, if your slope is positive go up or if it is negative go down whatever the RISE is. Go over to the right for the run. Mark the spot with a point.

• Draw a line thru those two points

Y= 2/3 x + 3

• Go to the y-axis and draw a point at 3.• From that point go up 2 units and over 3 units.

Draw a point.• Draw a line thru those two points.• That is how easy it is to graph lines.

Y = -3x -1

• Go to the y-axis and draw a point at –1.• From that point go down 3 units and over 1.

Draw a point.• Draw a line thru those points.• Wow that was easy!

Y= 2

• Draw out a two column box. The first column is labeled X and the second column is labeled Y.

• Fill the Y column with values of 2 because the equation said so.

• Pick any values for x.• Now graph those ordered pairs and draw a

line thru those points.

X= -4

• Make a chart again like last time.• But, All the values for x are –4’s. Because our

equation said so.• You decide the values for the y’s.• Now graph the ordered pairs and draw a line

thru those points.

Practice converting linear equations into Slope-Intercept

Form

It’s easier than you think…

Slope intercept form is:

y = mx + b

Our main goal is to get the y alone on one side of the

equation

Convert Into Slope-Intercept Form

2 4 2y x 2 2

2 4 2y x 2 2 2

(divide both sides by 2 to get y alone)

2 4 2y x

(now simplify all fractions)2 1

2 1y x

When an equation is in slope-intercept form:

What is the slope? ____________

2 1y x Now look at the equation below……

What is the intercept? ____________

1 2 3 4 5

1

2

3

4

5

-1

-2

-3

-4

-5

-1-2-3-4-5 0

Step 1: Look at the y-intercept and plot where the graphs cross the “y” axis.

Now look at the graph of the line.

Step 2: Use the slope (rise/run) to determine the next point and plot.

Step 3: Draw a line through both points. Be sure to extend pass point and put arrow at both ends.

*** Easy ***

5y = 10x + 15Convert to Slope-Intercept Form:

(divide both sides by 5 to get y alone)

(now simplify all fractions)

y = 2x + 3 BRAVO!!

5 10 15y x 5 5

5 10 15y x 5 5 5

*** Now Try this Convert to Slope-

Intercept Form ***

-3y = -9x - 12

Step 1: divide both sides by -3 to get y alone

Step 2: Simplify all fractions

Step 3: Write your equation in y = mx + b

What is the slope? ____________

What is the intercept? ____________

*** Check Your Answer ***

-3y = -9x - 12 (divide both sides by -3 to get y alone)

(now simplify all fractions)

y = 3x + 4

-3 -3

-3y = -9x - 12-3 -3 -3

Slope = 3

Intercept = 4

Wow, you’re good at this!!

*** medium ***

21x – 7y =14Convert to Slope-Intercept Form:

(subtract both sides by 21x)

-7y = -21x + 14(now divide both sides by -7)

y = 3x – 2

(simplify all fractions)

21 -21xx

7 - 7 -7

2y + 26 = -6x

Step 1: Subtract both sides by 26

Step 2: Divide both sides by 2 to get y by itself

Step 3: Simplify all fractions

*** Now Try this Convert to Slope-Intercept

Form ***

What is the slope? ____________

What is the intercept? ____________

2y + 26 = -6x(subtract both sides by 26)

2y = -6x - 26(now divide both sides by 2

y = -3x - 13

(simplify all fractions)

You are a math wizard!

*** Check Your Answer ***

26 -26

2 2 2

Graphing Linear Equations

In Slope-Intercept Form

We have already seen that linear equations have two variables and when we plot all the (x,y) pairs that make the equation true we get a line.

In this section, instead of making a table, evaluating y for each x, plotting the points and making a line, we will use The Slope-Intercept Form of the equation to graph the line.

y=2x+1

y=−x−4

y=32x−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=32x−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=32x−2

using their y-intercepts and slopes.

y=2x+1

1) 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=32x−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