Slope Intercept Equation

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Slope is defined as raise over run. The slope of the line is very useful for finding the equation of the straight line. The slope of the line can be calculated given two points on the straight line. The slope intercept equation of a straight line is of the form y = mx + b; here m is the slope of the line and b is the y-intercept of the line.

Example 1: Fine the slope intercept equation of a straight line passing through (2, 3) and having the slope 5?

Solution: Given is the slope of the line = 5.

The slope intercept form of a line => y = mx + b.

Hence the line given is y = 5 x + b.

Here b is the unknown. Mentioned in the question is, line passes through (2, 3).

Therefore, 3 = 5 (2) + b; b = 3 -10 = -7.

Hence the equation in slope intercept form is y = 5x - 7.
 
Example 2: Fine the slope intercept equation of a straight line passing through (1, 5) and having the slope 6?

Solution: Given is the slope of the line = 6.

The slope intercept form of a line => y = mx + b.

Hence the line given is y = 6 x + b.

Here b is the unknown. Mentioned in the question is, line passes through (1, 5).

Therefore, 5 = 6 (1) + b; b = 5 - 6 = -1.

Hence the equation in slope intercept form is y = 6x - 1.
 

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