1. Section 3.3 Graphing Linear Functions
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2. Recall: the COORDINATE/CARTESIAN PLANE, ie, your grid graph
(+)ve y-axis x y -4 -3 -2 -1 1 2 3 4
Quadrant 2
Quadrant 1
(-)ve x-axis
(+)ve x-axis
(horizontal axis)
Quadrant 3
Quadrant 4
ORIGIN: point where x-axis and y-axis meet
Coord. = (0,0)
(-)ve y-axis
(vertical axis)
The “x-axis” is also known by its better name: INDEPENDENT AXIS
The “y-axis” is also known by its better name: DEPENDENT AXIS

3. I) Horizontal & Vertical Lines
A Horizontal line has an equation in the form of:
A Vertical line has an equation in the form of:
The y-coordinate of every point is “6”
The x-coordinate of every point is “-5”

4. II) Graphing Linear Functions
There are several ways to graph a line besides making a TOV
1st Method:
Find both the “x” and “y” intercepts of the line
Connect the two intercepts
2nd Method:
Find the slope and y-intercept
Slope  Slant of the line, steepness
Y-intercept  where the line crosses the y-intercept

5. III) X and Y intercepts
The X-intercept is where the line crosses the X-axis.
Any point on the X-axis has a y-coordinate of zero (x,0)
The Y-intercept is where the line crosses the Y-axis.
Any point on the Y-axis has a x-coordinate of zero (0,y)

6. Finding the X & Y intercepts
At the x-intercept, the y-coordinate is zero.
To find the x-intercept, make the “y-variable” equal to zero and solve for “x”
At the y-intercept, the x-coordinate is zero.
To find the y-intercept, make the “x-variable” equal to zero and solve for “y”
The x-intercept will be -10/4 = -2.5
The y-intercept will be -10/5 = -2

7. Ex: Graph the following line by finding the x & y intercepts
Find the x-intercept:
Find the y-intercept:

8. IV) Slope – intercept form:
When a linear function is written in the form of y = mx + b, the slope is the constant “m” that is multiplied to the “x” variable when “y” is isolated
The constant “b” is the y-intercept
Ex: Find the slope and y-intercept for the following equations:
Slope = 0.5
Slope = 2/3
Slope = - 3/4
Y-intercept = 7
Y-intercept = 11/3
Y-intercept = 3
This is a vertical line!!
This is not a Linear Function!!
Slope = 0
Slope is infinity or undefined
Y-intercept = 12
Degree of “x” is 2
No Y-intercepts

9. V) Graphing a Line with the Slope
Besides making a TOV, another way to graph a line is by finding a point on the Line, and then “apply” the slope to find other points
Ex: Graph the line:
Start at the y-intercept
Then apply the slope to find other points:
Connect the dots

10. Practice: Graph a Line:
Start at the Y-intercept
Then apply the slope to find other points:
Connect the dots

11. VI) Solving for Missing Constants
Given that the equation of a line is y=2x+k and that it crosses the point (3,10). Find the value of ‘k”
When given an equation with a missing constant, plug the coordinates of the point to solve for “k”
The equation of the line will be:

12. Plug the information into the formula
Practice: Given that the slope of a line is -1/2 and that it crosses the point (3,5), find the Y-intercept
Plug the information into the formula
Plug the coordinates of the point into the formula
The y-intercept is 6.5

13. Practice: Given info on each line from the left, match it with the correct linear function on the right:

14. Challenge Problem: Graph the following lines and determine the coordinates of the vertices of the triangle, then find the area:
Graph each line separately
The points where the lines intersect will be the vertices of the triangle
The area of this box is A=6x8=48
Now cut out these 3 triangles

15. A triangle has vertices at points A(3,0), b(8,0), and C(5,10)
A triangle has vertices at points A(3,0), b(8,0), and C(5,10). A line is drawn from the origin to cut the triangle in half. What is the equation of this line?
The centroid of a circle is a point that in the circle that contains the center of gravity
Any line that crosses the centroid of a triangle will cut the area of the triangle in half
To find the coordinates of the centroid, take the averages of all 3 x-coordinates and all 3 y-coordinates.

16. Q: Given the rectangle, how many squares does the diagonal cross?