EDEXCEL GCSE FOUNDATION MATHS - What is Y = mx + c

Edexcel GCSE Foundation Maths: Understanding Y = mx + c

The equation y = mx + c is a fundamental concept in GCSE Maths. It represents the equation of a straight line. Let's break down the elements:

• y: Represents the dependent variable, usually plotted on the vertical axis (y-axis).
• x: Represents the independent variable, usually plotted on the horizontal axis (x-axis).
• m: Represents the gradient of the line. The gradient indicates the steepness of the line. A positive gradient means the line slopes upwards from left to right, while a negative gradient means the line slopes downwards.
• c: Represents the y-intercept. The y-intercept is the point where the line crosses the y-axis.

Understanding Gradient (m)

The gradient is calculated by finding the change in y divided by the change in x between any two points on the line.

Formula: m = (y2 - y1) / (x2 - x1)

Example:

Imagine you have two points on a line: (2, 4) and (5, 10).

• x1 = 2, y1 = 4
• x2 = 5, y2 = 10

Substituting these values into the formula:

m = (10 - 4) / (5 - 2) = 6 / 3 = 2

Therefore, the gradient of the line is 2.

Understanding Y-intercept (c)

The y-intercept is the point where the line crosses the y-axis. This means the value of x is always 0 at this point.

Example:

If the equation of a line is y = 2x + 3, then the y-intercept is 3 because when x = 0, y = 3.

Using the Equation to Find Points

You can use the equation y = mx + c to find points on the line. Simply substitute different values of x into the equation and solve for y.

Example:

Consider the equation y = 2x + 1. Let's find the y-coordinate when x = 3.

y = 2(3) + 1 = 6 + 1 = 7

Therefore, when x = 3, y = 7. This means the point (3, 7) lies on the line.

Drawing the Line

To draw a line using the equation y = mx + c, you can follow these steps:

1. Find the y-intercept: This is the value of 'c' in the equation. Plot this point on the y-axis.
2. Use the gradient: The gradient 'm' tells you how many units to move up or down for every unit you move across. For example, if the gradient is 2, move up 2 units and across 1 unit. Plot this new point.
3. Draw the line: Connect the two points you've plotted with a straight line.

Example:

Draw the line represented by the equation y = 3x - 2.

1. The y-intercept is -2. Plot the point (0, -2) on the y-axis.
2. The gradient is 3. This means for every unit you move across, you move up 3 units. From the y-intercept, move 1 unit to the right and 3 units up, plotting the point (1, 1).
3. Connect the points (0, -2) and (1, 1) with a straight line.

Applications of y = mx + c

The equation y = mx + c has many applications in real-world scenarios, including:

• Speed, distance, and time: The relationship between distance, speed, and time can be represented by a linear equation.
• Finance: You can use linear equations to model interest rates and investment growth.
• Physics: Linear equations are used to describe the motion of objects, such as the relationship between velocity, acceleration, and time.

By understanding the components and applications of y = mx + c, you will be well-equipped to solve a variety of problems in your GCSE Maths course.