y = mx + c reads straight off
m is the gradient (steepness) and c is the y-intercept (where the line crosses the y-axis). Rearrange any line into this form before reading either off.
Parallel ⇒ same gradient; perpendicular ⇒ negative reciprocal
Parallel lines have equal m. For perpendicular lines the gradients multiply to −1, so the perpendicular gradient is −1/m (flip and change sign).
Gradient from two points
Gradient = (change in y) ÷ (change in x) = (y₂−y₁)/(x₂−x₁). Keep the points in the same order top and bottom.
Drawn from real examiner reports.
Thinking the gradient is "2.5x" or an equation, not a number
Examiners were "surprised that many do not actually know what the gradient is" — values like 2.5x or 5/2x were commonly given. The gradient is a single numerical value.
Using the wrong perpendicular gradient
Students gave m = 2 or m = −2 instead of the negative reciprocal, and forgot to rearrange the given equation into y = mx + c before reading the gradient.
Plotting a line inaccurately / confusing x = k with y = k
Lines such as x + y = 7 were started correctly at 7 on one axis but joined to 8 on the other; x = 2 was drawn instead of y = 2.
Use a small table of values or the intercepts
Examiners noted very few students used a table of values or substituted x = 0 and y = 0 to plot a line. For x + y = 7, plot (7, 0) and (0, 7) and join with a ruler.
Gradient of a line parallel to y = 4x + 1?
The grid shows a straight line. Each square is one unit. The line passes through the lattice points and , and crosses the -axis at . Use the graph to find the equation of the line in the form .
