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