Section 3.3 Graphing Linear Functions © Copyright all rights reserved to Homework depot: www.BCMath.ca

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

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”

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

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)

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

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

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

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

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

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:

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

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

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

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.

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