Representing Linear Nonproportional Relationships
Make a table of values for the equation y=2x+5 when x=-2,-1,0,1,2
y=1,3,5,7,9
Find the slope of the line using the points (0,4) and (-3,6).
Slope= -2/3
Where does a nonproportional graph start at?
Any coordinate besides (0,0).
Graph y=2/3x-1
Draw Graph
Determine if the graph represents a proportional or nonproportional relationship.
Make a table of values for the equation y=3/8x-5 when x=-8,0,8. Give 2 more x values and determine all y values.
x= 16,24
y=-8,-5,-2,1,4
Find the y-intercept of a line using the points (0,4) and (-3,6).
Y-intercept=4
What is another word for slope?
Rate of Change/Constant of Proportionality
Graph the equation y=-300x+2400.
Draw Graph
Determine if the following equation represent a proportional or nonproportional relationship. d=65t
Proportional.
Is the equation y=8x+12 proportional or nonproportional?
Nonproportional.
Find the slope and y-intercept of the line represented by the table.
X=2,4,6,8 & Y=22,32,42,52
Slope=5
Y-intercept=12
What is a linear equation?
A linear equation is an equation whose solutions form a straight line on a coordinate plane.
Identify the coordinates of four point on the line with each given slope and y-intercept. Slope =5 and y-intercept=-1
(0,-1,),(1,4),(2,9),(3,14) (For example)
Determine if the linear relationship represented by the table is a proportional or nonproportional relationship.
x=2,8,14 and y=30,90,150
Nonproportional
Make a table and graph the solutions of the equation y=-2x+1 when x= -1,0,1,2
y=3,1,-1,-3
Show table representation.
Find the cost to park for a day and the hourly rate to rent a paddleboat using the table of values.
Number of Hours=1,2,3,4 and Cost($)=17,29,41,53
$5 to park; $12 per hour.
What is the formula to find the slope-intercept form?
Y=__x+__ or y=mx+b
Identify the coordinates of four points on the line with each given slope and y-intercept. Slope=2/3 and y-intercept=-5
(0,-5),(3,-3),(6,-1)(9,1) (For example)
A linear relationship that passes through the point (0,0) is referred to as?
Proportional.
How can you choose values for x when making a table of values represent a real world situation?
Choose values that make sense in the context. For example, games played must be whole numbers.
How can you determine the slope and the y-intercept of a line from a graph?
Find the slope of the line using the coordinates of two points found on the graph. Then find the y-coordinate of the point where the graph crosses the y-axis.
What is a y-intercept?
Why might someone choose to use the y-intercept and the slope to graph a line?
You can easily identify the slope (m) and y-intercept (b) from the slope-intercept form y=__x+__ and quickly use them to locate two point that determine the line.
How are using graphs, equations, and tables similar when distinguishing between proportional and nonproportional linear relationships?
Proportional relationships exist if the y-intercepts for a graph and an equation are 0, and if the table has, or would have, a value of 0 for y when x is 0.