A relationship can arrive as a table, a graph, an equation, or a sentence. All four carry the same two numbers.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
The two numbers
The slope says how fast it changes; the intercept says where it starts.
Getting them from a table
The slope is the change in y between rows divided by the change in x. The intercept is the y when x is nought.
Then compare
Once both are in slope and intercept form, the comparison is just two pairs of numbers.
A table, a graph and an equation
The same linear relationship can be given as a table of values, a drawn line, or an equation. All three carry the same information; each makes something different easy to see. Being fluent in all three is a central goal of the year.
Finding slope and intercept from a table
The slope is the change in y divided by the change in x between any two rows. The intercept is the y-value when x is zero, which you may have to work backwards to find if the table does not include it.
Comparing relationships in different forms
To compare a line given by a graph with one given by an equation, put both in the same form — usually extract slope and intercept from each. Comparing directly across forms is where mistakes happen.
Each form has its use
Equations are precise and easy to compute with. Graphs show behaviour at a glance. Tables give exact values at specific points. Choosing which to present is a communication decision, and it depends on what the reader needs.
Step 2: Try It Yourself
Tap and try it out.
The slope is 2: for every 1 across, the line goes 2 up.
Step 3: Watch an Example
One step at a time.
Watch Ana Compare Two Plans
Plan A is y = 5x + 20. Plan B is a table: 0 costs 30, 2 costs 38.
- Step 1
Plan A has slope 5 and starts at 20.
Step 4: Your Turn
Practice makes it stick.
The Equation
Problem 1 of 2
In y = 7x + 4, what is the slope?
The Table
Problem 2 of 2
At x = 0, y = 12; at x = 3, y = 21. What is the slope?
Pull Out the Numbers
1 of 4
In y = 2x + 9, what is the starting value?
2 of 4
In y = −3x + 1, what is the slope?
3 of 4
At x = 0, y = 5; at x = 4, y = 17. What is the slope?
4 of 4
Of slopes 4 and 6, which relationship grows faster? Give the number.
Step 5: Quick Check
Show what you know.
Question 1 of 1
At x = 0, y = 8; at x = 5, y = 33. What is the slope?
What You Learned
- Every linear relationship carries a slope and a starting value.
- Both can be pulled out of a table, a graph, an equation, or a description.
- Once both are in that form, comparing them is comparing two pairs of numbers.