Equations of straight line graphs

When calculating equations of straight lines
Remember:

y = mx + c for any straight line, where m represents the gradient and c represents the y intercept.

The gradient represents the steepness of the graph.

To calculate the gradient of a line remember it is the difference in y divided by the difference in x or in simple terms up divided by across.















The y intercept is where the graph crosses the y axis in the above example the graph crosses the y-axis at the point 2, so the y intercept is 2.

If we put these two pieces of information together we can write the equation of a straight line.

The equation of the line shown above in the form y = mx + c is

y = 0.5x + 2

Obtaining the gradient and y intercept from an equation

If the equation is written in the form y = mx + c we can read the gradient and intercept straight from it

E.G:
1) y = 3x + 5, gradient = 3, y intercept = 5

2) y = 4 - 5x, gradient = - 5, y intercept = 4

If the equation is not in the form y = mx + c we may have to rearrange

E.G

3) 2y = 8x - 4
if we divide everything by 2 we get
y = 4x - 2 and we can now obtain the gradient as 4 and y intercept as -2

4) 3y + 6x = 12

First move the 6x from the LHS by subtracting it from both sides

3y = 12 - 6x

then divide by 3 to leave you with

y = 4 - 2x, the gradient is -2 and the y intercept is 4.