# How To: Determine the equation of a line

Learn how to determine the equation of a line with this tutorial:

The equation of a line can be determined by two given conditions.

1. The line passing through a single point with a given slope.
2. The line passing through two points.

1. Equation of the line passing through a single point and a given slope.
To find the equation of a line passing through the point (2,5) and having a slope of 2.
The equation of a line can be defined as,

y = mx + b

where :

* m is the slope, and
* b is the y-intercept

Now since m is the slope and the given value of which is 2, substitute the value of m in the equation i.e.

y = mx + b will read as y = 2x + b

To find the value of b, the y-intercept first understand the meaning of given value (2,5)

* (2,5)means when x of a line is 2, the y of the line must be 5 Now one can find the value of b by substituting the values in the equation y = mx + b

i.e. 5 = 2 X 2 + b therefore 5 - 4 = b and the value of b will be 1

Hence the equation of a line passing through the points (2,5) with a slope of 2 is y = 2x + 1

2. To find the equation of a line passing through two points.

Make use of the following formula:

m = (y2 - y1) / (x2 - x1)

Now find the value of m by substituting the values of x and y and then resubstitute the value of m in the following equation:

y1 = m (x1) + b

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