Gradient and Y-Intercept in Linear Equations

Q: What do m and c represent in y = mx + c?

In y = mx + c, m represents the gradient and c represents the y-intercept. The gradient m measures how steep the line is and which way it slants. The y-intercept c tells you where the line crosses the y-axis. Together, these two values describe the whole straight line.

Q: What does the gradient (m) tell you about a line?

The gradient m tells you how much the line rises or falls for each step you take to the right. A positive m makes the line rise from left to right, while a negative m makes it fall from left to right. The further m is from 0, the steeper the line becomes.

Q: What happens when the gradient is 0?

When the gradient m is 0, the value of y always equals c, whatever value x takes. This produces a flat, horizontal line that crosses the y-axis at c. The line never rises or falls, because there is no change in y as you move to the right.

Q: Why does the line cross the y-axis at c?

The line crosses the y-axis at the point where x is 0. If you substitute x = 0 into y = mx + c, you get y = m × 0 + c, which simplifies to y = c. So the constant c is always the y-intercept of the line.

Q: What does it mean when c is 0?

When c is 0, the equation simplifies to y = mx. With no constant to shift it up or down, the line passes straight through the origin, the point (0, 0). The gradient m still controls how steep the line is and which way it slants.

Q: How many points do you need to draw a straight line?

You only need 2 points to draw a straight line. Plot the y-intercept first using c, then use the gradient m to step across to a second point. Join the two points with a ruler and extend the line across your graph.

Key concept

Gradient (m) and y-intercept (c) are the two parts of a straight line y = mx + c. The gradient shows how steep the line is, so m = 2 means y rises 2 as x rises 1. The y-intercept is where the line crosses the y-axis, at x = 0.

Gradient and Y-Intercept in Linear Equations - introduction visual

Video Lesson

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$Gradient and Y-Intercept in Linear Equations poster$

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Flashcards

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Linear equation y = mx + c showing the gradient (m) and y-intercept (c), with a graph of a straight line.

Linear equation y=mx+c with highlighted y-intercept c where line crosses y-axis. Diagram shows lines with different y-intercepts, one passing origin.

Graph illustrating y = mx + c with explanations of gradient (m) and y-intercept (c), and examples of positive and negative gradients.

How to draw a linear equation with gradient (m) and y-intercept (c) shown on a graph, step-by-step guide with illustrations.

Steps to draw a linear equation y = -3x + 4, find y-intercept at 4, move 1 step right and 3 steps down, and connect points with the line.

Recap: Linear Equations

Linear equations are usually written in the form y = mx + c.
When you draw a linear equation, it makes a straight line on a graph.

Practice Questions

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Q1Easy

What is the slope (m) of the line for the equation $y = - 4 x + 3$ ?

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Interactive Activity

Gradient and Y-Intercept in linear equations

Plotting y = mx + c

Linear Equation

Gradient (m)2

Controls the slope ("rise")

Y-Intercept (c)1

Controls the start height

How to draw it:

Step 1: Plot the y-intercept (1) on the vertical axis.
Step 2: Move 1 unit right, then move 2 units up.
Step 3: Connect the points to form the line.

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Students Also Ask

The questions students bump into most on this topic

What do m and c represent in y = mx + c?

In y = mx + c, m represents the gradient and c represents the y-intercept. The gradient m measures how steep the line is and which way it slants. The y-intercept c tells you where the line crosses the y-axis. Together, these two values describe the whole straight line.

What does the gradient (m) tell you about a line?

The gradient m tells you how much the line rises or falls for each step you take to the right. A positive m makes the line rise from left to right, while a negative m makes it fall from left to right. The further m is from 0, the steeper the line becomes.

What happens when the gradient is 0?

When the gradient m is 0, the value of y always equals c, whatever value x takes. This produces a flat, horizontal line that crosses the y-axis at c. The line never rises or falls, because there is no change in y as you move to the right.

Why does the line cross the y-axis at c?

The line crosses the y-axis at the point where x is 0. If you substitute x = 0 into y = mx + c, you get y = m × 0 + c, which simplifies to y = c. So the constant c is always the y-intercept of the line.

What does it mean when c is 0?

When c is 0, the equation simplifies to y = mx. With no constant to shift it up or down, the line passes straight through the origin, the point (0, 0). The gradient m still controls how steep the line is and which way it slants.

How many points do you need to draw a straight line?

You only need 2 points to draw a straight line. Plot the y-intercept first using c, then use the gradient m to step across to a second point. Join the two points with a ruler and extend the line across your graph.

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