Key Concepts

Key Concepts

• The slope–intercept form of an equation of a line with slope \(m\) and y-intercept, \(\left(0,b\right)\) is, \(y=mx+b\).
• Graph a Line Using its Slope and y-Intercept
  
  1. Find the slope-intercept form of the equation of the line.
  2. Identify the slope and y-intercept.
  3. Plot the y-intercept.
  4. Use the slope formula \(m=\frac{\text{rise}}{\text{run}}\) to identify the rise and the run.
  5. Starting at the y-intercept, count out the rise and run to mark the second point.
  6. Connect the points with a line.
• Strategy for Choosing the Most Convenient Method to Graph a Line: Consider the form of the equation.
  
  • If it only has one variable, it is a vertical or horizontal line.
    \(x=a\) is a vertical line passing through the x-axis at \(a\).
    \(y=b\) is a horizontal line passing through the y-axis at \(b\).
  • If \(y\) is isolated on one side of the equation, in the form \(y=mx+b\), graph by using the slope and y-intercept.
    Identify the slope and y-intercept and then graph.
  • If the equation is of the form \(Ax+By=C\), find the intercepts.
    Find the x- and y-intercepts, a third point, and then graph.
• Parallel lines are lines in the same plane that do not intersect.
  
  • Parallel lines have the same slope and different y-intercepts.
  • If m₁ and m₂ are the slopes of two parallel lines then \({m}_{1}={m}_{2}.\)
  • Parallel vertical lines have different x-intercepts.
• Perpendicular lines are lines in the same plane that form a right angle.
  
  • If \({m}_{1}\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}{m}_{2}\) are the slopes of two perpendicular lines, then \({m}_{1}·{m}_{2}=-1\) and \({m}_{1}=\frac{-1}{{m}_{2}}\).
  • Vertical lines and horizontal lines are always perpendicular to each other.

Glossary

parallel lines

Lines in the same plane that do not intersect.

perpendicular lines

Lines in the same plane that form a right angle.

slope-intercept form of an equation of a line

The slope–intercept form of an equation of a line with slope m and y-intercept, $(0,b)$ is, $y=mx+b$.