Graph Linear Equations

How do we graph linear equations?

In the last section, we looked at how to solve for the slope of an equation and how to solve for the y-intercept.

Now we are going to look at how to graph these lines

Remember….

To solve for the slope, we use the formula

Once we solve for the slope, we can use that and a point to solve for the y-intercept using the slope intercept form

12

12

xx

yym

bmxy

Let’s try a few reminder problems

(3,4) and (-2,3) (7,4) and (4,3)

5

17

5

15

175

34

)3(5

14

5

1

5

1

32

43

xy

b

b

b

bmxy

m

3

5

3

13

53

43

)4(3

13

3

1

74

43

xy

b

b

b

bmxy

m

Now how do we graph these equations?

First, look at the y-intercept. This will be your starting point. Graph this point.**Note** Your y-intercept will be on the y-axis

Once you have plotted the y-intercept, use your slope to formulate the rest of the line. Remember

Run

RiseSlope

Let’s Look at a Few Examples!

Graph the line y=-3x+5 Graph the line y=2x+2

Now you try a Few Examples

Graph y=3x+2 Graph y=-2x-4

What happens if….

What happens in our equation is not in slope intercept form?

Sometimes our equations might be in standard form.

Never fear, we can still graph them!!

How?

There are 2 ways we can go about graphing an equation from standard form

First, we can try and find the x and y intercepts of the line and plot those points and fill in the line

Second, we can solve the equation and put it in slope intercept form.

Let’s try

Take the equation 4x-y-7=0, for instance.

First, get x and y alone: 4x-y=7

To find the x intercept, let y=0. So x=7/4

To find the y intercept, let x=0, so y=-7

Therefore our 2 points are (7/4, 0) and (0,-7)

Use the same equation and put it in slope intercept form.

4x-y=74x=y+7y=4x-7

Both of these cases, we can graph. When using standard form, plot the points!

When using slope intercept form, graph the intercept and then the slope!

Let’s try together! 2x+3y=6Let x=0, y=2Let y=0, x=3

x+4y-8=0 x+4y=8Let x=0, y=2Let y=0, x=8

Now you try!-2x+5y=10Let y=0, x=-5Let x=0, y=2

3x+9y=9Let y=0, x=3Let x=0, y=1