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Study Guides > ALGEBRA / TRIG I

Introduction to Writing Equations of Lines

What you'll learn to do: Write equations of lines.

Just as there are many ways to get from your home to the grocery store, there are different ways to write the equation of a line. For example, sometimes you will know where the line crosses the y-axis (the y-intercept), while at other times you might only know the location for two points on a line.  Depending upon what information about the line you are given, you can figure out the equation of a line by using what you know about the line. So far, we have learned how to use a coordinate plane to graph points and lines, we have used tables and intercepts to plot lines on the coordinate plane, and we have learned that an important part of a line is the slope. All of this information has helped us draw graphs of lines and learn about the different qualities that make different lines.  In this section we will learn about writing the equation of a line in different formats using what we already know. In this section, we will also learn about parallel and perpendicular lines.  When you graph two or more linear equations in a coordinate plane, they generally cross at a point. However, when two lines in a coordinate plane never cross, they are called parallel lines. We will explore the slopes and equations of parallel lines, as well as construct equations of lines that are parallel to a given line. Additionally, in this section you will look at when two lines in a coordinate plane cross at a right angle. These are called perpendicular lines. The slopes of the lines in each of these cases have a special relationship to each other. You will learn how to write the equation of a line that is perpendicular to a given line. Specifically, in this section you’ll learn how to:
  • Write the equation and draw the graph of a line using slope and y-intercept
  • Write and solve equations of lines using slope and a point on the line
  • Write and solve equations of lines using two points on the line
  • Identify slopes of parallel and perpendicular lines
  • Write equations of parallel and perpendicular lines


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