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.
Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.