Unit 5: Writing Linear Equations

STANDARD FORM: Ax+By=C

An equation is in standard form if: A, B, and C are integers: NO fractions or decimals Variables are on one side of the constant (#) is on the other The coefficient of x must be greater than or = to 0. (A>0) Greatest Common Factor = 1 (if A, B, and C contain a common factor, divide each term by the common factor, make sure that all of your variables are integers!)

Parallel line

Parallel lines have the same slope and different y-intercepts

To put an equation into standard form:

1) Get rid of the fractions - Multiply all terms by the least common denominator 2) Move the variable terms to the same side 3) Coefficient of x should be positive. If not see below. If the coefficient of x is a negative number, take the opposite of every term in the linear equation

Given SLOPE and ONE POINT on the line

1) Slope = m ; Ordered Pair (x1, y1) 2) Substitute thes values into POINT-SLOPE FORM: y-y1=m(x-x1) 3) Simplify and write the equation in the asked for format when necessary

Given SLOPE and Y-INTERCEPT of the line

1) Slope = m' y-intercept = b 2) Substitute these values into SLOPE-INTERCEPT FORM: y=mx+b 3) Write the equation in standard form when necessary

Given TWO POINTS

1) find the slope of the line Slope = y2-y1/x2-x1

Horizontal Line

The slope of a horizontal line is zero It's equation is y = #. (Note: This line crosses through the y-axis) Ex: Write the equation of a horizontal line that passes through the point (-6, 11) Ex: Write the equation of a horizontal line that passes through the point (21, -54)

Vertical Line

The slope of a vertical line is undefined It's equation is x = #. (Note: This line crosses through the x-axis) Ex: Write the equation of a vertical line that passes through the point (-8, 42) Ex: Write the equation of a vertical line that passes through the point (73, -81)

Perpendicular line

This product of perpendicular line' slopes is -1 Therefore the slopes of perpendicular lines are _________ and _______ of one another