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 − y₁ = m(x − x₁)

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 = –3x − 6
y = –3x − 6 + 1
y = –3x − 5

The required equation is y = –3x − 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 2y = –3x – 7

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