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Distributed Linear Equations


Linear equations are equations that describe a line on a graph. A linear equation will tell you the slope of the line (how steeply it rises or falls) and the point at which the line crosses the y-axis (where x=0). The most common form of displaying a linear equation is using the template y=mx+b, where m is the slope and b is the intercept.

Distributing an equation means multiplying out the parentheses. If you have a set of parentheses in an equation, you won't be able to solve it until you have multiplied them out.



Distributing means multiplying out the parenthesis in an equation. For example, if you are given the equation 2(x+3) = 10, you can distribute the two by multiplying it with both of the terms inside the parenthesis to get:

2x+6=102x + 6 = 10

Then you subtract 6 from both sides to get the like terms together:

2x+6(6)=10(6)2x + 6 (-6) = 10 (-6)

2x=42x = 4

x=2x = 2

Remember, to do this with a linear equation, we need to get the y value on its own on the left of the equation (just y, not 2y, or y2y^{2}) and the x value and the number on the right of the equation.

So, if we get the equation:

y=4(x1)y = 4(x - 1)

We would need to distribute in order to solve.

Firstly, we multiply the 4 by both terms inside the parenthesis:

y=4(x)+4(1)y = 4(x) + 4(-1)

y=4x4y = 4x - 4

Since 'solving' a linear equation just means putting it in y=mx+b format, we have now solved it.

A key point to remember is that if the number outside the parenthesis is negative, we need to distribute that too.

For example:

y= -8( 12 rac{1}{2} x + 2)

We would need to multiply the -8 by both terms inside the parenthesis:

y=8(y= -8(12 rac{1}{2}x)+8(2)x) + -8(2)

y=4x16y = -4x-16


9(4x+5)=1719(4x + 5) = -171
9(4x+5)9(4x + 5)==171-171
36x+4536x + 45==171-171

Distributed Linear Equations Worksheets (PDF)

Distributed Linear Equations Worksheet 1

Distributed Linear Equations Worksheet 2

Distributed Linear Equations Worksheet 3