By: Anna Carey, Ali LaBella, and Jen Putnam

SOLVING LINEAR EQUATIONS

A linear equation is an equation that has no operations other than

addition, subtraction, and multiplication of a variable by a

constant.

LINEAR EQUATIONS

VS.LINEAR

FUNCTIONS

Linear Equations Not Linear Equations

7x − 3y = 14 8a + 3b2 = -12

x = 11y=ghghjgfj

3s = -2t − 9 x + xy = 2

y = ¼x y = 1/X

EXAMPLES OF LINEAR EQUATIONS

Linear Equations cannot…• Be raised to a power other than 1• Cannot have two variables multiplied by

each other

WHY?

Ax + By = C• A must be greater than or equal to zero• A and B cannot be zero• Example: 5x + 7y = 12

STANDARD FORM

y = mx + b • m is the slope of the line• b is the y-intercept• Example: y = ¾x + 6

SLOPE-INTERCEPT FORM

y − y1 = m(x − x1)• (x1 , y1) are the coordinates of a point on

the line• m is the slope of the line• Example: y +1 = ¼(x − 2)

POINT-SLOPE FORM

x/a + y/b = 1• a is the x-intercept• b is the y-intercept• Example: x/2 + y/5 = 1

INTERCEPT FORM

• Slope is the ratio of the change in y-coordinates to the change in x-coordinates. (Rise over Run, Rate of Change)

y2 − y1 = m

x2 − x1tghr

WHAT IS SLOPE?

• The x-intercept is where the line crosses the

x-axis.• Set y equal to zero• Example: 4x + 2y = 8

4x + 2(0) = 8 4x = 8 x = 2

• So, the x-intercept is (2, 0)

FINDING THE X-INTERCEPT

• The y-intercept is where the line crosses the

y-axis.• Set x equal to zero• Example: 4x + 2y = 8

4(0) + 2y = 8 2y = 8 y = 4

• So, the y-intercept is (0, 4)

FINDING THE Y-

INTERCEPT

Solve: 3x − 4 = -101. Isolate the variable, x

3x − 4 (+ 4) = -10 (+ 4)

3x = -6

x = -2

The solution to this linear equation is x = -2

SOLVING A LINEAR EQUATION