ParaPro Math Study Guide: Linear Equations & Coordinate Planes

To solve a linear equation, you should isolate the variable.  You are trying to determine what value of the variable would make the equation true.

To isolate the variable, you use inverse operations (addition and subtraction or multiplication and division).

The = symbol represents equality.  Whatever you do to the left side of the equals symbol you need to do to the right side of the equals symbol.

Example 1

$x + 5 = 12$

To isolate the variable $(x)$, you undo adding $5$ by subtracting $5$ from both sides of the equation.

$x + 5 \ – \ 5 = 12 \ – \ 5 \ \ → \ \ x = 7$

Example 2

$b \ – 19 = 20$

To isolate the variable $(b)$, you undo subtracting $19$ by adding $19$ to both sides of the equation.

$b \ – 19 + 19 = 20 + 19 \ \ → \ \ b = 39$

Example 3

$3k = 24$

To isolate the variable $(k)$, you undo multiplying by $3$ by dividing both sides of the equation by $3$.

$ \dfrac{3k}{3} = \dfrac{24}{3} \ \ → \ \ k = 8$

Example 4

$ \dfrac{x}{4} = 16$

To isolate the variable $(x)$, you undo dividing by $4$ by multiplying both sides of the equation by $4$.

$4 * \dfrac{x}{4} = 16*4\ \ → \ \ x = 64$

Coordinate Planes

The coordinate plane is the space created by the x-axis (horizontal axis) and the y-axis (vertical axis).

The center of the coordinate plane is known as the origin (0,0).

To locate a point on the coordinate plane, the coordinate pair (x,y) indicates how far to move left or right (x) and up or down (y) from the origin.

Example 1

$(2,4)$

The point $(2,4)$ is located by going $2$ units to the right and $4$ units up from the origin.

Example 2

$(-3,-1)$

The point $(-3,-1)$ is located by going $3$ units to the left and $1$ unit down from the origin.

Linear Equations & Coordinate Planes Review Test



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