Drawing linear graphs
Section: Coordinate geometry | Syllabus: Cambridge IGCSE Mathematics (0580)
Drawing a Straight-Line Graph from Its Equation
A straight-line graph can be drawn accurately by finding just two points that satisfy its equation, plotting them, and joining them with a single ruled line.
- Substitute the two endpoints of the given x-range into the equation to find two points on the line
- Plot both points accurately, then join them with a single ruled straight line drawn across the full width of the grid
- As a check, the line should also pass through its y-intercept (found by substituting x = 0)
Worked Example: Drawing a Line from Its Equation
- Question: On a grid, draw the graph of y=1.5x-2 for -2 x4.
- Step 1: When x = -2: y=1.5(-2)-2=-5
- Step 2: When x = 4: y=1.5(4)-2=4
- Step 3: Plot (-2, -5) and (4, 4), then join them with a single ruled line across the full width of the grid
- Answer: line drawn through (-2, -5) and (4, 4); it should also pass through (0, -2), the y-intercept, as a check
Common Mistakes
MistakePlotting the two points correctly but joining them with a short line segment instead of extending it across the whole grid
Fixrule the line across the full width of the grid provided, not just between the two calculated points
MistakeMaking a sign error when substituting a negative x-value, especially when the gradient is also negative
Fixwork through the substitution one operation at a time, keeping track of each sign carefully
Drawing Horizontal and Vertical Lines
Horizontal and vertical lines are special cases of straight-line graphs - each has a fixed coordinate that never changes, no matter how far the line is drawn.
- A horizontal line has equation y = c, where every point on the line has the same y-coordinate, c
- A vertical line has equation x = c, where every point on the line has the same x-coordinate, c
- A horizontal line has a gradient of 0; a vertical line has an undefined gradient (it cannot be measured, since there is no change in x)
Worked Example: Drawing a Horizontal and a Vertical Line
- Question: On the same grid, draw the lines y = 4 and x = -3.
- Step 1: For y = 4, every point on the line has y-coordinate 4 - draw a horizontal line straight across the grid at height 4
- Step 2: For x = -3, every point on the line has x-coordinate -3 - draw a vertical line straight down the grid at x = -3
- Answer: two straight lines drawn - one horizontal through y = 4, one vertical through x = -3, crossing at the single point (-3, 4)
Common Mistakes
MistakeConfusing which equation gives a horizontal line and which gives a vertical line, e.g. drawing y = 4 as a vertical line
Fixy = c is horizontal (y is fixed while x varies); x = c is vertical (x is fixed while y varies) - the letter that is fixed tells you the line's direction
MistakeTrying to find a gradient and y-intercept for a vertical line the same way as for other lines
Fixa vertical line has no gradient (it is undefined) and does not have a y-intercept in the usual sense unless it is the y-axis itself
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