Graph Linear Equations

1. Graph Linear Equations

2. 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

3. 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

4. (3,4) and (-2,3) (7,4) and (4,3) Let’s try a few reminder problems

5. 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

6. Graph the line y=-3x+5 Graph the line y=2x+2 Let’s Look at a Few Examples! 

7. Graph y=3x+2 Graph y=-2x-4 Now you try a Few Examples 

8. 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!!

9. 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.

10. 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=7 4x=y+7 y=4x-7 Let’s try 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!

11. 2x+3y=6 Let x=0, y=2 Let y=0, x=3 x+4y-8=0 x+4y=8 Let x=0, y=2 Let y=0, x=8 Let’s try together! 

12. -2x+5y=10 Let y=0, x=-5 Let x=0, y=2 3x+9y=9 Let y=0, x=3 Let x=0, y=1 Now you try!