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Line Equation

Point-slope and Slope-intercept forms of a line

These are two common formulations for the equation for a line.

Slope-intercept
 form of a line is:
y=mx+b
It is useful if you want to know the slope, m, and, well, the y-intercept of the line, b.  Conversely, you can find the equation for this line if you know the slope and y-intercept.

Point-slope form of a line is:
y-y1=m(x-x1)
where (x1,y1) is a point on the line.
This version of the equation for a line is useful if you know the slope of the line, and a point on the line, or conversely, you can derive this equation if you know slope and a point.

How to derive Point-slope:
slope is defined as rise over run, or change in y divided by change in x
slope = m = change in y  =  y-y1
                       change in x      x-x1
So you get
m  =  y-y1
          x-x1
If you multiply both sides by (x-x1), you end up with the point-slope formula for a line:
y-y1 = m(x-x1)

Note that you can convert between the two forms.
Point-slope to slope intercept: just solve for y, and simplify the other side.
y-y1 = m(x-x1)
y=y1+ m(x-x1)
y=y1+ mx -mx1
y=mx +(y1-mx1)
y=mx +     b
So that the y-intercept is y1-mx1.

To go from slope-intercept to point-slope, just plug in a number for x, and find the corresponding y value.  Plug these in for x1 and y1, and use the point-slope formula.

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  • Home
  • GMAT
    • Your Best Option for Private GMAT Tutoring >
      • The Value of GMAT Tutoring with Test Prep Unlimited
    • Flat Fee Score Guarantee
    • What's Included in the Full GMAT Course
    • How Much Time We Save You
    • How Much Will My Score Increase After A NonTPU GMAT Class/Course?
    • When To Hire An Expert Private GMAT Tutor >
      • Why You Shouldn't Hire An Inexperienced GMAT Tutor
  • Contact
  • Resources
    • Referral Program
    • TPU GMAT Blog
    • TPU GMAT Forum
    • GMAT Myths Debunked
    • How To Structure Your Study
  • About
    • The TPU Team Approach
    • Credentials
    • Inspirational Math Story
    • CEO Bio
    • Jobs >
      • Description
      • Application