## Key Concepts

- We can solve linear equations in one variable in the form [latex]ax+b=0[/latex] using standard algebraic properties.
- A rational expression is a quotient of two polynomials. We use the LCD to clear the fractions from an equation.
- All solutions to a rational equation should be verified within the original equation to avoid an undefined term, or zero in the denominator.
- Given two points, we can find the slope of a line using the slope formula.
- We can identify the slope and
*y*-intercept of an equation in slope-intercept form. - We can find the equation of a line given the slope and a point.
- We can also find the equation of a line given two points. Find the slope and use the point-slope formula.
- The standard form of a line has no fractions.
- Horizontal lines have a slope of zero and are defined as [latex]y=c[/latex], where
*c*is a constant. - Vertical lines have an undefined slope (zero in the denominator), and are defined as [latex]x=c[/latex], where
*c*is a constant. - Parallel lines have the same slope and different
*y-*intercepts. - Perpendicular lines have slopes that are negative reciprocals of each other unless one is horizontal and the other is vertical.

## Glossary

**conditional equation** an equation that is true for some values of the variable

**identity equation** an equation that is true for all values of the variable

**inconsistent equation** an equation producing a false result

**linear equation** an algebraic equation in which each term is either a constant or the product of a constant and the first power of a variable

**solution set** the set of all solutions to an equation

**slope** the change in *y-*values over the change in *x-*values

**rational equation** an equation consisting of a fraction of polynomials