4.6 Find the equation of a line  (Page 5/7)

In [link] , we used the point–slope form to find the equation. We could have looked at this in a different way.

We want to find a line that is perpendicular to $x=5$ that contains the point $\left(3,\mathrm{-2}\right)$ . The graph shows us the line $x=5$ and the point $\left(3,\mathrm{-2}\right)$ .

We know every line perpendicular to a vetical line is horizontal, so we will sketch the horizontal line through $\left(3,\mathrm{-2}\right)$ .

Do the lines appear perpendicular?

If we look at a few points on this horizontal line, we notice they all have y -coordinates of $\mathrm{-2}$ . So, the equation of the line perpendicular to the vertical line $x=5$ is $y=\mathrm{-2}$ .

Key concepts

• To Find an Equation of a Line Given the Slope and a Point
  1. Identify the slope.
  2. Identify the point.
  3. Substitute the values into the point-slope form, $y-y_1=m\left(x-x_1\right)$ .
  4. Write the equation in slope-intercept form.

  
  
  

• To Find an Equation of a Line Given Two Points
  1. Find the slope using the given points.
  2. Choose one point.
  3. Substitute the values into the point-slope form, $y-y_1=m\left(x-x_1\right)$ .
  4. Write the equation in slope-intercept form.

  
  
  

• To Write and Equation of a Line
  • If given slope and y -intercept, use slope–intercept form $y=mx+b$ .
  • If given slope and a point, use point–slope form $y-y_1=m\left(x-x_1\right)$ .
  • If given two points, use point–slope form $y-y_1=m\left(x-x_1\right)$ .

  
  
  

• To Find an Equation of a Line Parallel to a Given Line
  1. Find the slope of the given line.
  2. Find the slope of the parallel line.
  3. Identify the point.
  4. Substitute the values into the point-slope form, $y-y_1=m\left(x-x_1\right)$ .
  5. Write the equation in slope-intercept form.

  
  
  

• To Find an Equation of a Line Perpendicular to a Given Line
  1. Find the slope of the given line.
  2. Find the slope of the perpendicular line.
  3. Identify the point.
  4. Substitute the values into the point-slope form, $y-y_1=m\left(x-x_1\right)$ .
  5. Write the equation in slope-intercept form.

Practice makes perfect

Find an Equation of the Line Given the Slope and y -Intercept

In the following exercises, find the equation of a line with given slope and y-intercept. Write the equation in slope–intercept form.