Graphs

Summary and Exam Tips for Graphs

Graphs is a subtopic of Algebra, which falls under the subject Mathematics in the Edexcel Lower Secondary curriculum. In graphing linear functions, the equation $8x + 4y = 12$ is first solved for $y$, resulting in $y = -2x + 3$. Here, $x$ is the independent variable and $y$ is the dependent variable. To graph, choose at least two $x$-values, including zero, negative, and positive numbers, to find corresponding $y$-values. Plot these points on a Cartesian plane and draw a line through them, extending indefinitely with arrows. The slope of the line, denoted by $m$, is determined by the rise over the run between any two points $(x_1, y_1)$ and $(x_2, y_2)$. For simultaneous equations like $x + y = 3$ and $y = 2x - 6$, plotting both on the same axes shows their intersection point, which satisfies both equations. When plotting linear graphs, construct a table of values by substituting $x$ into the equation, then plot and connect the points to form a straight line. This method is essential for understanding the relationship between algebraic expressions and their graphical representations.

Exam Tips

• Understand Variables: Remember that in linear equations, $x$ is the independent variable and $y$ is the dependent variable.
• Choose Diverse $x$-Values: When plotting graphs, select a range of $x$-values, including negative, zero, and positive, to ensure a comprehensive graph.
• Plot Accurately: Use a ruler to draw straight lines and add arrows to indicate the graph extends indefinitely.
• Slope Calculation: Practice calculating the slope $m$ using the rise over run formula between two points.
• Intersection Points: For simultaneous equations, focus on finding the intersection point, as it represents the solution to both equations.