18 Key Concepts & Glossary

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