The Cartesian Plane
How many quadrants does the cartesian plane have?
4
What is a rule?
An equation which describes the relationship between two or more variables/pronumerals.
List the coefficient and constant of this equation/rule:
y = 3x + 2
Coefficient: 3
Constant: 2
Substitute y = 7 into the rule y = 2x - 3, and solve algebraically to find the x-coordinate.
x = 11
The x-intercept is found when y = what?
And
The y=intercept is found when x = what?
y = 0
And
x = 0
What is a point on a number plane called?
Hint: (x,y)
Coordinates
For the rule y = 3x + 1, find the y-coordinate for these x-coordinates:
a. 1
b. 0
c. -5
d. 11
a. y = 4
b. y = 1
c. y = -14
d. y = 34
Come up with three examples of rules.
Hint: Remember a rule typically starts with y = ____.
Teacher checks answer.
State the coordinates (x, y) of the point on this graph
of y = 2x where:
a. 2x = 4 (i.e. y = 4)
b. 2x = 6.4
c. 2x = −4.6
d. 2x = 7
a. (2, 4)
b. (3.2, 6.4)
c. (-2.3, -4.6)
d. (3.5, 7)
Fill in the blank:
Find the x -_____ by substituting y = ___ into the rule.
Find the x-intercept by substituting y = 0 into the rule.
What is the point (0,0) called?
The origin (O).
State the missing number in this table for the rule y = 5x + 2
x | -3 | -2 | -1 | 0 |
y | | -8 | -3 | 2 |
y = -13
Fill in the blanks:
To find the rule of a table of values, find the ch___ in the y-values (bottom row) and what the y-value is when __= 0.
To find the rule of a table of values, find the change in the y-values (bottom row) and what the y-value is when x = 0.
For each of these graphs state the coordinates of the point of intersection (i.e. the point where
the lines cross over each other).
a. P.O.I = (4, 3)
b. P.O.I = (-2, -3)
State the x- and y-intercepts of this table:
x | -2 | -1 | 0 | 1 | 2 |
y | 2 | 0 | -2 | -4 | -6 |
x-intercept = -1
y-intercept = -2
A(2,3), B(0,1), C(-2,2), D(-3,0), E(-3,-4), F(4,-3)
Teacher will check graph.
Draw a graph and plot these points given the rule and table of values:
y = 2x - 2
x | -2 | -1 | 0 | 1 | 2 |
y | -6 | -4 | -2 | 0 | 2 |
Teacher will check graph.
Find the rule for this table of values:
x | -2 | -1 | 0 | 1 | 2 |
y | -8 | -5 | -2 | 1 | 4 |
y = 3x - 2
Use the graph of y = 2x + 1, to solve each of
the following equations.
a. 2x + 1 = 5
b. 2x + 1 = 0
c. 2x + 1 = − 4
a. x = 2
b. x = -0.5
c. x = -2.5
Solve these equations for x:
a. 0 = x− 4
b. 0 = x + 2
c. 0 = 2x + 10
a. x = 4
b. x = -2
c. x = -5
Find the midpoint of this line segment: (1,3) and (3,5).
Hint: Plot the points on a graph, connect them, and find the point in the middle.
(2,4)
Do the points (1, 3) and (-2, -4) lie on the graph of y = 3x?
Hint: Use substitution and don't forget (x, y).
(1, 3) lies on the graph.
(-2, -4) does not lie on the graph.
Find the rule for this table of values:
x | 3 | 4 | 5 | 6 | 7 |
y | -5 | -7 | -9 | -11 | -13 |
y = -2x + 1
Find the point of intersection (P.O.I) of the graph for the rules: y = 4 - x and y = 2x + 1
P.O.I = (1, 3)
Find the x- and y- intercepts of this rule:
y = 3x − 6
Hint: Use substitution.
y-intercept = -6