# Find the Equation Of A Line Given Its Slope And A Point On The Line

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In this lesson, we will learn how to get the equation of a line given its slope and a point on the line by

- using the Point-Slope Form.
- substituting into the Slope-Intercept equation.

## Using the Point-Slope Form to get the Equation

We will now look at how to use the point-slope form to get the equation of a line given its slope and a point on the line.

**Example*** : *

Find the equation of a line with slope –3 and passing through (–2, 1).

** ***Solution: *

** Step 1** : Write out the Point-slope Form

* y* − *y*_{1} = *m*(*x *−* x*_{1})

** Step 2** : Substitute the slope –3 and the coordinates of the point (–2, 1) into the point-slope form.

*y* − 1 = –3(*x *−(−2))

** Step 3** : Simplify the equation

*y* − 1 = –3(*x *−(−2))

*y* − 1 = –3(*x * + 2)

*y* − 1 = –3*x * − 6

*y* = –3*x * − 6 + 1

*y* = –3*x * − 5

The required equation is *y* = –3*x * − 5

This video looks at writing linear equations in point-slope form, given a point and a slope, or two points. It includes four examples.

## Using the Slope-Intercept to get the Equation

**Example*** : *

Find the equation of a line with slope – and passing through (–3, 1).

*Solution: *

** Step 1: ** Substitute *m* = – , *x* = –3 and *y* = 1 into the equation *y* = *mx+ c *to obtain the value of *c*.

** Step 2: ** Write out the equation of the line

The required equation is or 2*y* = –3*x* – 7

This will show you how to write an equation of a line that has a given slope and passes through a given point.

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