How to Convert Linear Equations
Linear equations are the most basic form of algebraic equation. These equations contain no other operations other than addition/subtraction or multiplication/division, and are graphed as a straight line. Linear equations come in many forms, including standard form, point-slope form and slope-intercept form. However, it is the slope-intercept form that is often the most useful, especially when graphing. If an equation is presented in a form other than slope-intercept form, it is fairly simple to convert it. The goal of converting a linear equation is to isolate the "Y." This works the same as solving any other algebraic equation. However, instead of getting a number for an answer, you will have a whole equation.
Other People Are Reading
Instructions
-
-
1
To begin converting a linear equation, move all of the "Y"s to one side of the equation and all of the "X"s to the other. Make sure to combine any like terms first. For instance, if the equation is (4Y + 3)/9 + 6X = 8 + 2X, you would subtract 6X from both sides so that the "X"s are moved to the right to get (4Y+3)/9 = 8 - 4X.
-
2
Look for any parentheses and remember that a long division bar means that there are parentheses around the top and bottom. If there are parentheses on the side with the "X"s, go ahead and use the distributive property to get rid of them. If there are parentheses on the side of the equation containing the "Y"s, perform the opposite operation of the one that is attached to the parentheses. In the example equation, the parentheses are on the Y side and involve division, so you would do the opposite and multiply both sides by 9 to get 4Y + 3 = 8 - 4X.
-
-
3
Now focus on the side of the equation that contains the "Y"s. If there is a number added or subtracted on that side, do the opposite to both sides. With 4Y + 3 = 8 - 4X, you need to subtract 3 from both sides so the equation looks like this: 4Y = 5 - 4X.
-
4
Divide everything by the number in front of the "Y," if there is one. In this case, you divide everything by 4 and end up with Y = 5/4 - X.
-
5
Understand that, to finish converting a linear equation into slope-intercept form, the "Y" must be on the left side, and the X and plain number (constant) need to be in the proper order on the right-hand side. The "X"s come first. Remember that, when you move a number or variable around, a negative sign in front has to travel with it. So the example equation would end up looking like this when converted to slope-intercept form: Y = -X + 5/4.
-
1
Tips & Warnings
The constant or plain number on the right-hand side when the equation is converted is the y intercept. The number in front of the "X" is the slope, and describes how steep the line of the linear equation is.
