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Graphing a line from its equation

Plot the intercept, then use rise over run to find the next point.

The common mistake

Starting at the origin instead of at b, or running the slope the wrong way for a negative value.

Instead: Start at (0, b). For slope a/b, go up a (down if negative) and right b, then join the points.

Worked example with Guide me

Graph y = −2x + 3.

  1. Sugar · Where do we start?
    Student · At (0, 3).
  2. Sugar · Slope −2 means?
    Student · Down 2, right 1.
  3. Sugar · So the next point?
    Student · (1, 1).

Answer: A line through (0, 3) and (1, 1).

Try 3 practice questions

  1. 1. Name two points on y = x − 4.

    Show answer

    (0, −4) and (1, −3)

  2. 2. Name two points on y = ½x + 1.

    Show answer

    (0, 1) and (2, 2)

  3. 3. Where does y = 3x − 6 cross the x-axis?

    Show answer

    (2, 0)

Quick answers

What is the most common mistake with graphing a line from its equation?
Starting at the origin instead of at b, or running the slope the wrong way for a negative value.
How do I get graphing a line from its equation right?
Start at (0, b). For slope a/b, go up a (down if negative) and right b, then join the points.
Can you show a worked example?
Graph y = −2x + 3. A line through (0, 3) and (1, 1).

Related concepts

Save this as a miss — practice it before your test

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Save this as a miss — practice it before your test