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Forms of linear equations review

There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form. We review all three in this article.
There are three main forms of linear equations.
Slope-interceptPoint-slopeStandard
y=mx+byy1=m(xx1)Ax+By=C
where m is slope and b is the y-interceptwhere m is slope and (x1,y1) is a point on the linewhere A, B, and C are constants

Example

A line passes through the points (2,4) and (5,5). Find the equation of the line in all three forms listed above.
Two of the forms require slope, so let's find that first.
slope=m=ΔyΔx=5(4)5(2)=93=3
Now we can plug in m and one of the points, say (5,5), to get point-slope form, yy1=m(xx1):
yy1=m(xx1)y5=3(x(5))y5=3(x+5)
Solving for y, we get slope-intercept form, y=mx+b:
y5=3(x+5)y5=3x15y=3x10
And adding 3x to both sides, we get standard form, Ax+By=C:
y+3x=10
Want another example? Check out this video.
Want to practice the different forms yourself? Check out this exercise.
Want a more in-depth review of each form? Check out these review articles: