1. Graphing Linear Equations
EQ – How do we plot points and graph linear equations?
Graphing Linear Equations
Slope Intercept Form

2. A Little review…

3. COORDINATE PLANE QUAD II QUAD I QUAD III QUAD IV Y-axis
Parts of a plane
X-axis
Y-axis
Origin
Quadrants I-IV
QUAD II
QUAD I
Origin ( 0 , 0 )
X-axis
QUAD III
QUAD IV

4. PLOTTING POINTS
Remember when plotting points you always start at the origin. Next you go left (if x-coordinate is negative) or right (if x-coordinate is positive. Then you go up (if y-coordinate is positive) or down (if y-coordinate is negative) B C A D
Plot these 4 points
A (3, -4), B (5, 6), C (-4, 5) and D (-7, -5)

5. SLOPE
Slope is the ratio of the vertical rise to the horizontal run between any two points on a line. Usually referred to as the rise over run.
Run is 6 because we went to the right
Slope triangle between two points. Notice that the slope triangle can be drawn two different ways.
Rise is 10 because we went up
Rise is -10 because we went down
Run is -6 because we went to the left
Another way to find slope

6. FORMULA FOR FINDING SLOPE
The formula is used when you know two points of a line.
EXAMPLE

7. X AND Y INTERCEPTS
The x-intercept is the x-coordinate of a point where the graph crosses the x-axis.
The y-intercept is the y-coordinate of a point where the graph crosses the y-axis.
The x-intercept would be 4 and is located at the point (4, 0).
The y-intercept is 3 and is located at the point (0, 3).

8. SLOPE-INTERCEPT FORM OF A LINE
The slope intercept form of a line is y = mx + b, where “m” represents the slope of the line and “b” represents the y-intercept.
When an equation is in slope-intercept form the “y” is always on one side by itself. It can not be more than one y either.
If a line is not in slope-intercept form, then we must solve for “y” to get it there.
Examples

9. NOT IN SLOPE-INTERCEPT
y = 3x – 5
y – x = 10
y = -2x + 10
2y – 8 = 6x
y = -.5x – 2
y + 4 = 2x
Put y – x = 10 into slope-intercept form
Add x to both sides and would get y = x + 10
Put 2y – 8 = 6x into slope-intercept form.
Add 8 to both sides then divide by 2 and would get y = 3x + 4
Put y + 4 = 2x into slope-intercept form.
Subtract 4 from both sides and would get y = 2x – 4.

10. GRAPHING LINES BY MAKING A TABLE
I could refer to the table method by input-output table or x-y table. For now I want you to include three values in your table. A negative number, zero, and a positive number.
INPUT (X)
OUTPUT (Y) -2 -4 2 1 5
Graph y = 3x + 2
By making a table it gives me three points, in this case (-2, -4) (0, 2) and (1, 5) to plot and draw the line.
See the graph.

11. Plot (-2, -4), (0, 2) and (1, 5)
Then draw the line. Make sure your line covers the graph and has arrows on both ends. Be sure to use a ruler.
Slope-intercept graphing

12. Slope-intercept graphing
Steps
Make sure the equation is in slope-intercept form.
Identify the slope and y-intercept.
Plot the y-intercept.
From the y-intercept use the slope to get another point to draw the line.
y = 3x + 2
Slope = 3 (note that this means the fraction or rise over run could be (3/1) or (-3/-1). The y-intercept is 2.
Plot (0, 2)
From the y-intercept, we are going rise 3 and run 1 since the slope was 3/1.