Linear Functions & Graphing

Master linear functions, their standard form, and how to graph them on the coordinate plane.

8th Grade

Algebra

~45 min

🎮 Interactive Activity: Linear Function Grapher

Explore how slope and y-intercept affect the graph!

y = 2x + +1

Slope (m) = 2, Y-intercept (b) = 1

🎮 Interactive Activity: Slope Calculator

Calculate slope from two points!

Points: (1, 2) and (3, 6)

Formula: m = (y₂ - y₁) / (x₂ - x₁)

1. What is a Linear Function?

📚 Linear Function Definition

A linear function is a function whose graph is a straight line. It can be written in the form:

y = mx + b

• m = slope (rate of change)

• b = y-intercept (where line crosses y-axis)

• x = input variable

• y = output variable

2. Standard Form and Slope-Intercept Form

3. Graphing Linear Functions

4. X and Y Intercepts

5. Parallel and Perpendicular Lines

6. Real-World Applications

7. Worked Examples

8. Frequently Asked Questions

Practice Time!

Practice Quiz

Questions

Correct

Score

What is the general form of a linear function?

○

What is the y-intercept of y = 3x - 5?

○

What is the slope of the line passing through (2, 3) and (4, 7)?

○

Which line has a positive slope?

○

What is the x-intercept of y = 2x + 4?

○

If a line has slope 0, what type of line is it?

○

What is the equation of a line with slope -3 and y-intercept 2?

○

Two lines are parallel if they have:

○

What is the slope of y = 5?

○

If f(x) = 4x - 7, what is f(3)?

○