Writing Equations in Slope Intercept Form

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Equations of a line can be written in many forms such as the standard form, slope-intercept form, point-slope form etc. These forms express the equation of a line in different ways and represent a line in various equation forms. Slope-intercept form of a line is written by taking the slope and the y-intercept of a line and it is written as: y = mx + b, where ‘m’ is the slope of the line, ‘b’ is the y-intercept and, ‘x’ and ‘y’ are the variables of the equation.

 Example 1: Write the equation of a line in slope-intercept form which has a slope of 2 and the point where the line intersects the Y-axis as (0, 5).

Given: slope of the line, m = 2

The point where the line crosses the Y-axis is known as the y – intercept.

Given the point (0, 5) -> this gives the y-intercept, b = 5

Slope-intercept form of a line -> y = mx + b

Using the above equation, we get: y = 2x + 5

Therefore the equation of the line is y = 2x + 5.
 
Example 2: Write the equation of a line in slope-intercept form which has a slope of 4 and the point where the line intersects the Y-axis as (0, -2).

Given: slope of the line, m = 4

The point where the line crosses the Y-axis is known as the y – intercept.

Given the point (0, -2) -> this gives the y-intercept, b = -2

Slope-intercept form of a line -> y = mx + b

Using the above equation, we get: y = 4x + (-2)

Therefore the equation of the line is y = 4x – 2.

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