2.2.4

# Finding Equation

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## Finding the Equation of a Line From a Graph

We can calculate the equation of a line if we have two points on the line or one point and the gradient.

### Given two points - method

• To find the equation of a line between two points, first calculate the gradient m.
• Then substitute in one of the points into the equation and rearrange to find c.
• For example to find the equation of the line between (2,4) and (-1,2)...

### Given two points - step 1

• Find the gradient:
• change in y = 4 - 2 = 2
• change in x = 2 - (-1) = 3
• so m = 23

### Given two points - step 2

• We know the line is y = 23x + c so substitute in x = 2 and y = 4 to find c:
• (4) = 23(2) + c
• so c = 83
• Therefore the line is y = 23x + 83.

### Given gradient and point

• To find the equation of a line with a given gradient and going through a point substitute in the point to the line y = mx + c where m is the gradient you’ve been given.

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