2.2 Linear equations in one variable  (Page 7/15)

Key concepts

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

Section exercises

Verbal

Algebraic

For the following exercises, solve the equation for $x.$