Transcript Linear Equations and Graphs

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Relation
Input
Output
Function
Domain
Range
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Scatter Plot
Linear Equation
x - intercept
y- intercept
Slope
Rise
Run
Relation: a set of ordered pairs that relates an input to an
output.
Input: a number on which a function operates.
Output: a number produced by evaluating a function using a
given input.
Function: a pairing of each number in a given set with exactly
one number in another set.
Domain: the set of all possible input values for the function.
Range: the set of all possible output values for a function.
Scatter plot: The graph of a set of data pairs (x,y), which is a
collection of points in a coordinate plane.
Slope: is the ratio of the rise (vertical change) to the run
(horizontal change) between any two points on the line.
Rise: the vertical change between two points on a line.
Run: the horizontal change between two points on a line.
x - intercept: the x coordinate of the point where the graph
intersects the x-axis.
y - intercept: the y coordinate of the point where the graph
intersects the y-axis.
Input
Output
x
y
2
3
4
4
6
5
8
6
10
7
Function
Rule
y = 1/2x + 2
Domain
2, 4, 6, 8, 10
Range
3, 4, 5, 6, 7
Use the form y= mx + b
in which m is the slope
and b is the y- intercept
Find the value of m.
m= change in output
change in input
Substitute the value
of m into the form
y= mx + b
Substitute an input – output pair
for x and y to find the value of b
or
Use the m to find the value of
y when x = o
Substitute the value
of b into the form
y= mx + b
x
y
1
4
2
7
3
10
4
13
Use the form y= mx + b
Find the value of m.
m= (7-4) = 3 = 3
(2-1) 1
Substitute for m
y= 3x + b
Use an input output pair to
substitute for x and y
(1,4)
4 = 3 (1) + b
4=3+b
4 – 3 = 3 -3 + b
1=b
Substitute for b
y= 3x + 1
Choose several values to substitute for x.
Substitute for x into the function rule.
Solve for y to find the output for each input.
Write the input and output as a pair in the table.
y = 4x - 2
x
y
1
2
2
x = 1 , 2, 3, 4
y = 4 (1) - 2
y = 4 (1) – 2
y=4–2
y = 2 when x = 1
3
4
Choose several values to substitute for x.
List the solution in a table as ordered pairs.
Plot the ordered pairs.
Draw a line through them.
(3,6)
y = 3x - 3.
(2,3)
(0,-3)
(1,0)
x = 0, 1, 2, 3
x
y
0
-3
1
0
2
3
3
6
Plot the ordered pairs.
Draw a line through them.
Plot the order pairs from the table.
Label the horizontal and vertical axes.
Identify the relationship that exists between two sets of
data.
The y – coordinates increases
as the x – coordinates
increases.
The y – coordinates decreases
as the x – coordinates
increases.
No obvious pattern exists
between the coordinates.