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
* 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