Equation of a Straight Line
Grade 5y = mx + c
Every straight line on a coordinate grid has an equation of the form:
y = mx + c
where m is the gradient and c is the y-intercept (where the line crosses the y-axis). Read the gradient and y-intercept straight from the equation once it is in this form.
Finding the equation from two points
Step 1: calculate the gradient using the two points. Step 2: substitute one point and the gradient into y = mx + c to find c. Step 3: write the full equation.
Parallel and perpendicular lines
Parallel lines have equal gradients. Perpendicular lines have gradients that are negative reciprocals of each other — if one has gradient m, the perpendicular has gradient −1/m. Their product is always −1.
To find the negative reciprocal: flip the fraction and change the sign. Gradient 3 → perpendicular gradient −1/3. Gradient −2/5 → perpendicular gradient 5/2.
Worked example
EXAMPLE
Find the equation of the line through (1, 5) and (3, 11).
Gradient = (11 − 5) ÷ (3 − 1) = 6 ÷ 2 = 3. Using y = mx + c with point (1, 5): 5 = 3(1) + c, so c = 2. Equation: y = 3x + 2.
