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What Is the Linear Functions?(With Examples)

A linear function is a function whose graph is a straight line. It can be written in the form f(x) = mx + b, where m is the slope and b is the y-intercept. Linear functions have a constant rate of change.

Grades 8-9 (Algebra)Key Stage 3-4Årskurs 8-9Klasse 8-9

📖Definition

📐Formula

f(x) = mx + b

In f(x) = mx + b: m is the slope (rate of change), b is the y-intercept (where the line crosses the y-axis), x is the input, and f(x) is the output.

📝Step-by-Step Guide

Identify the Form

Write the function in slope-intercept form f(x) = mx + b.

Find Slope and Y-Intercept

The coefficient of x is the slope (m). The constant is the y-intercept (b).

Graph the Function

Plot the y-intercept, then use the slope to find more points. Connect with a straight line.

Evaluate the Function

To find f(a), substitute a for x and calculate.

f(a) = m(a) + b

⚠️Common Mistakes to Avoid

Confusing f(x) with f times x
Misidentifying slope and y-intercept
Plotting points incorrectly
Forgetting that linear means constant rate of change
Not recognizing equivalent forms of linear functions

✏️Practice Problems

Easy

For f(x) = 2x + 3, find f(4)

Answer: 11

Medium

Find the slope and y-intercept of f(x) = -3x + 7

Answer: Slope = -3, y-intercept = 7

Hard

A linear function has f(2) = 5 and f(5) = 14. Find the function.

Answer: f(x) = 3x - 1

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Worked Examples

Graph a Linear Functionmedium

Linear Equations Slope Functions Graphing

Curriculum Alignment

CommonCore (8.F.A.3)KS3KMK

Classroom assessment context

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