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Graphing Linear Equations

And Inequalities

Create an x y chart. Pick the x’s that you would like to use. You must pick at least three, you may

pick more. Remember, small numbers close to zero

work best. Find the y values by plugging your x

values into the given equation and solve for y.

Graph your points and draw your line.

Graph using an x y chart

2x – 4y = 12

x y-1 0 1

-3.5 -3-2.5

Find the x-intercept of the line by setting y = 0.

The x-intercept can be written as a point (x , 0)

Find the y-intercept of the line by setting x = 0.

The y-intercept can be written as a point (0 , y)

Plot the x and y intercepts on your graph and connect the two points.

You only need two points for this method only.

Graph using x and y intercepts

2x – 4y = 12x-int : 2x – 4(0) =

12 x-int = 6 pt (6 , 0)Y-int : 2(0) – 4y = 12 y-int = -3 pt (0, -3)

Start your graph at the given point. Count your slope from the given point. Connect your points to graph your line.

Graph with the slope and a point

Point (-3 , 6), slope =

Rearrange any linear equation into y = mx + b form.

Plot the y-intercept or b on the y-axis. Count the slope from the y-intercept. Positive slopes go up and to the right or

down and to the left. (either positive, positive or negative, negative)

Negative slopes go up and to the left or down and to the right. (either positive, negative or negative, positive)

Remember that any whole number or integer slope is over 1. (Example: a slope of 5 is )Graph using y = mx

+ b

3x – 5y = -15-3x -3x-5y = -3x - 15 -5 -5y = x + 3

Graph the same as lines. You will graph a solid line with ≤ or ≥. You will graph a dotted line with < or >. Shade above the line for ≥ or >. Shade below the line for ≤ or <. Check your solution by plugging a point

in. If the point works in your line then your graph should be shaded to that side. (0 , 0) is the best point to use

Graph Inequalities

y ≤ -3x - 4