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




 
Related Topics:
More Lessons for Geometry

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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

yy1 = 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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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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