What is a linear graph in the context of Edexcel IGCSE Mathematics?

In Edexcel IGCSE Mathematics, a linear graph represents a straight line on a coordinate plane. It is defined by a linear equation of the form y = mx + c, where m is the gradient (slope) and c is the y-intercept. Linear graphs are fundamental in understanding relationships between variables in sequences, functions, and graphs.

How do you find the gradient of a linear graph?

The gradient of a linear graph, often referred to as the slope, measures the steepness of the line. It is calculated by the formula m = (change in y) / (change in x), or rise over run. This can be determined by selecting two points on the line and dividing the difference in their y-coordinates by the difference in their x-coordinates.

What is the significance of the y-intercept in a linear equation?

The y-intercept of a linear equation is the point where the graph crosses the y-axis. In the equation y = mx + c, the y-intercept is represented by c. It indicates the value of y when x is zero, providing a starting point for graphing the line and understanding its position on the coordinate plane.

How can you determine if two linear graphs are parallel?

Two linear graphs are parallel if they have the same gradient but different y-intercepts. This means their equations will have the same value for m in y = mx + c, but different values for c. Parallel lines never intersect and maintain a constant distance apart.

What is the process for graphing a linear equation on a coordinate plane?

To graph a linear equation on a coordinate plane, start by identifying the y-intercept (c) and plot it on the y-axis. Then, use the gradient (m) to determine the direction and steepness of the line. From the y-intercept, move vertically and horizontally according to the gradient to plot a second point. Draw a straight line through these points to complete the graph.

Linear Graphs | Edexcel IGCSE Mathematics

Summary and Exam Tips for Linear Graphs

Linear Graphs is a subtopic of Sequences, Functions, and Graphs, which falls under the subject Mathematics in the Edexcel IGCSE curriculum. This topic focuses on understanding and interpreting both linear and non-linear graphs, using Cartesian coordinates, and plotting points in all four quadrants. Key concepts include determining the coordinates of points, calculating the midpoint and length of line segments using the Pythagorean theorem, and recognizing the equations of lines. The gradient, a measure of a line's steepness, is crucial for identifying parallel and perpendicular lines. For parallel lines, gradients are equal, while for perpendicular lines, the product of their gradients is $-1$ . The equation of a straight line is typically expressed in the form $y = mx + c$ , where $m$ is the gradient and $c$ is the y-intercept. Understanding these concepts is essential for solving problems related to linear graphs, such as finding the equation of a line, determining distances, and identifying relationships between lines.

Exam Tips

Understand the Cartesian Plane: Familiarize yourself with plotting points and interpreting coordinates in all four quadrants of the Cartesian plane.
Master the Gradient: Remember that the gradient ( $m$ ) is calculated as the change in $y$ over the change in $x$ . This is essential for identifying parallel and perpendicular lines.
Equation of a Line: Practice deriving the equation of a line using the formula $y = mx + c$ , and understand how to find the x- and y-intercepts.
Midpoint and Distance: Use the midpoint formula $\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$ and the distance formula derived from the Pythagorean theorem to solve problems involving line segments.
Parallel and Perpendicular Lines: Remember that parallel lines have equal gradients, while the product of the gradients of perpendicular lines is $-1$ . This is crucial for solving related exam questions.

By focusing on these key areas, you'll be well-prepared to tackle questions on linear graphs in your exams.

Linear Graphs

Video Library for Linear Graphs

Exam Tips and Study Notes for Linear Graphs