Drawing straight line graphs

Drawing Straight Line Graphs

Concepts

• Straight line graphs are visual representations of linear equations in the form of y = mx + c.
• The coordinate grid or Cartesian plane, comprises the x-axis (horizontal) and y-axis (vertical) intersecting at the origin (0,0).

Getting Started

• Begin by identifying the equation of the line you need to plot.
• Determine ‘m’ (gradient) and ‘c’ (y-intercept) from the equation.

Plotting the Y-Intercept

• Y-intercept ‘c’ is the point where the line crosses the y-axis.
• To find it, set ‘x’ to 0 and solve for ‘y’ in the given equation.
• Mark the y-intercept on the y-axis.

Applying the Gradient

• Gradient ‘m’ tells us how much ‘y’ changes for each unit increase in ‘x’.
• If the gradient is positive, move up from the y-intercept; if negative, move down.
• For each unit moved horizontally to the right, move ‘m’ units vertically, based on the direction identified by the sign of the gradient.
• Mark this new point, resulting from the gradient, on the graph.

Drawing the Line

• Draw the line by using a ruler to make a straight line through the y-intercept and the point identified by the gradient.
• This line is a visual representation of all solutions to the equation y = mx + c.

Checking Your Work

• Always ensure the line passes through the y-intercept ‘c’ and accurately represents the gradient ‘m’.
• Check your work by picking a point on the line and confirming it satisfies the equation.

Reading Straight Line Graphs

• Interpreting graphs can help to understand the relationship between variables in an equation.
• A steeper gradient implies a larger rate of change.
• The y-intercept gives the value of ‘y’ when ‘x’ is 0.
• The position and steepness of the graph tell us about the signs and magnitudes of ‘m’ and ‘c’ in the equation y = mx + c.