1. What is the equation of a straight line?
The equation that produces a straight line on a graph is called an equation of a straight line. In general form an equation of straight line looks like
y = mx + c
Where m is the gradient of the equation which tells you about the angle it makes with the x-axis and c is a constant that gives you the y-intercept.
To calculate the gradient we use this formula
Write down the gradient of the line with equation y = 2x + 3.
The general form of a line is y = mx + c by comparing with this we know that gradient (m) = 2
A straight line has gradient 3 and passes through the point (2,10).
Work out the equation of the line.
Let the equation of the line is y = mx + c
Gradient (m) = 3
so equation became y = 3x + c
Now as it passes through (2,10) putting
y = 10 and x = 2
10 = 3 × 2 + c
c = 10 - 6 = 4
so the equation of the line is
y = 3x + 4
This graph shows part of a straight line.
a) show that the gradient of this line is 3.
b) write down the equation of the line.
