Every straight line can be written y = mx + b.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
What m does
m is the slope. It sets how steep the line is and which way it tilts.
What b does
b is where the line crosses the vertical axis, the value of y when x is zero.
When b is zero
y = mx passes through the origin, which is exactly the proportional relationship of Grade 7.
What each letter does
In y = mx + b, the m is the slope — how much y changes for each unit of x — and b is the y-intercept, the value of y when x is zero. Two numbers determine the entire line.
Graphing from the equation
Plot the intercept at (0, b), then use the slope to step to a second point: right 1, up m. Two points give the line. This takes seconds and is far more reliable than building a table of values.
When b is zero
If b = 0 the line passes through the origin and the relationship is proportional — the Grade 7 special case. Every proportional relationship is linear; the b is what allows linear relationships that are not proportional.
What the numbers mean in a situation
For a taxi charging £3 plus £2 per mile, the cost is y = 2x + 3: the slope is the per-mile rate and the intercept is the fixed charge. Naming what m and b represent is usually the most useful thing to say about a model.
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 Leo Read a Line
Leo is given y = −3x + 5.
- Step 1
He reads m as −3, so the line falls 3 for every 1 across.
Step 4: Your Turn
Practice makes it stick.
The Value
Problem 1 of 2
y = 4x + 3. What is y when x = 5?
The Intercept
Problem 2 of 2
y = 7x − 2. What is y when x = 0?
Read the Equation
1 of 4
y = 2x + 7. What is the slope?
2 of 4
y = 2x + 7. What is y when x = 0?
3 of 4
y = −x + 4. What is y when x = 3?
4 of 4
y = 5x. Does it pass through the origin?
Step 5: Quick Check
Show what you know.
Question 1 of 2
y = 3x − 4. What is y when x = 6?
Question 2 of 2
In y = mx + b, what does b tell you?
What You Learned
- Every line can be written y = mx + b.
- m is the slope and b is where it crosses.
- When b is zero the relationship is proportional.