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Point Slope Applet
applet
Overview of different forms of a line's equation
There are many different ways that you can express the equation of a line. There is the slope intercept form , standard form and also this page's topic-point slope form. Each one expresses the equation of a line, and each one has its own pros and cons. Point Slope form, this page's topic, makes it easy to find the line's equation when you only know the slope and a single point on the line(see example 1).. Point slope form is also the quickest method for finding the equation of line given two points (see example 2).
Definition of the Point Slope Form Equation
The Point Slope Form Formula:
Example and Non Example Equations

Examples of Point Slope Form Equations Non-Examples
y −5 = 3(x −2) 2y = 4x +2
y + 5= ½(x − 12) x = 6 − y
y + 5= 4(x + 12) y = 2x + 7
y + ½= ¼(x + ¾) 3x + 5y = 2


When is point slope form useful?



When are other forms more useful?

  • Standard Form is more convenient when you know or need to know the x intercept and also the y-intercept and do not know the slope
  • Slope intercept form is best when you know the slope and the y-intercept .
  • Video Tutorial on Point Slope Form
    Slope Intercept Form
    Point Slope Form
    Standard Form
    Toggle Points
    Slope?
    Show Rise and Run ?
    $$ $$ $$ $$




    Practice Problems


    Problem 1) Identify which equations below are in point slope form
    • Equation 1: 2x + 2y =6
    • Equation 2: y - 5 = 3(x -2)
    • Equation 3: y =2x + 3
    • Equation 4: y + 3 = 3(x - ½)
    Answer


    Problem 2) Which equations below are in point slope form
    • Equation 1: y − 2 = 3(x − 4)
    • Equation 2: y + 5= (x − 4)
    • Equation 3: y = 3(x − 4) +2
    • Equation 4: y − 2 = 3(x − 4)
    Answer

    How to Solve common point slope form questions
    Example 1: Find equation given slope and 1 point
    Write the point slope equation of a line with slope 3 that passes through the point (-2, 5).
    1)Substitute slope for 'm' and the coordinates for x1 and y1 into the formula y − y1= m(x − x1)
    y − 5 = 3(x − -2)
    y − 5 = 3(x + 2 )
    Yes , it really is that easy to write the equation of a line in point slope form when you know its slope and 1 point on the line! . This should be a real relief to those of you who are used to doing this with slope intercept form , which would require 2 more steps (i.e. substitute a point and solve for b').


    Example 2: Find equation given 2 points
    Write the point slope equation of a line that goes through the points (1 , 7 ) and ( 5 , 19 ) .
    1) Calculate the slope m (slope) =
    2) Substitute slope for 'm' and the coordinates for x1 and y1 into the formula (you can use either point) y − y1= m(x − x1)
    y − 7 = 3(x − 1 )
    Or if you use the 2nd point
    y − 5 = 3(x − 19 )
    Practice writing equations in point slope form

    Problem 1)Write the point slope equation of a line that has a slope of 5 and that goes through the point (1, 4).
    Answer


    Write the point slope equation for the line in the graph below.
    Step 1
    1) Pick any 2 points on the line and calculate the slope
    Step 2
    2)Substitute slope for 'm' and the coordinates for x1 and y1 into the formula (you can use either point ) y − y1= m(x − x1)
    y −-2 = (x − 3 )
    y + 2 = (x − 3 )
    Or if you use the 2nd point
    y − 0= −(x −6)
    y= (x − 6)

    Point Slope Form Graph1
    Practice writing equations in point slope form

    Problem 1)Write the point slope equation of a line that has a slope of -3and that goes through the point (-4, 7).
    Answer


    Problem 2) Write the point slope equation of a line that goes through the points (2, 6) and ( 4, 7).
    Answer


    Problem 3) Write the point slope equation of a line that has a slope of ½ and that goes through the point (3, −4).
    Answer


    Problem 4) Write the point slope equation of a line that goes through the points (-6, -1) and ( 9 , -11).
    Answer

    Other Types of Problems

    There are a many other question types that involve point slope form. Try some of the ones below to see how you do.
    Write the point slope equation for the line in the graph below.
    Step 1
    1) Pick any 2 points on the line and calculate the slope
    Step 2
    2)Substitute slope for 'm' and the coordinates for x1 and y1 into the formula (you can use either point ) y − y1= m(x − x1)
    y −1 = −½(x −3 )
    Or if you can use the 2nd point
    y − 01= −½(x − 5)
    y= −½(x − 5)

    Point Slope Form Graph1