4.5 Use the slope–intercept form of an equation of a line  (Page 8/12)

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 m ₁ and m ₂ 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 $m_1\text{and}{m}_2$ are the slopes of two perpendicular lines, then $m_1·m_2=\mathrm{-1}$ and $m_1=\frac{\mathrm{-1}}{m_2}$ .
  • Vertical lines and horizontal lines are always perpendicular to each other.

Practice makes perfect

Recognize the Relation Between the Graph and the Slope–Intercept Form of an Equation of a Line

In the following exercises, use the graph to find the slope and y-intercept of each line. Compare the values to the equation $y=mx+b$ .

$y=3x-5$

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$y=4x-2$

slope $m=4$ and y -intercept $\left(0,\mathrm{-2}\right)$

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$y=\text{−}x+4$

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$y=\mathrm{-3}x+1$

slope $m=\mathrm{-3}$ and y -intercept $\left(0,1\right)$

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$y=-\frac{4}{3}x+1$

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$y=-\frac{2}{5}x+3$

slope $m=-\frac{2}{4}$ and y -intercept $\left(0,3\right)$

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Identify the Slope and y-Intercept From an Equation of a Line

In the following exercises, identify the slope and y-intercept of each line.

Graph a Line Using Its Slope and Intercept

In the following exercises, graph the line of each equation using its slope and y-intercept.

Choose the Most Convenient Method to Graph a Line

In the following exercises, determine the most convenient method to graph each line.

Graph and Interpret Applications of Slope–Intercept