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Lesson · Grade 8 · Mathematics

Graphing y = 2x − 3 with Negative Coordinates

  • Grade 8
  • Mathematics
  • 2 min 9 s
  • British Columbia
  • BC8-MA-18

Students build a table of values for y = 2x − 3 from x = −2 to 3, working out each y step by step, then turn each row into an ordered pair and plot it from the origin, where a negative x means go left and a negative y means go down. A dashed line shows that all six points line up, which makes the relation linear, and two common mistakes, dropping the signs to get (1, 5) and swapping x and y to get (−5, −1), are shown as points far off the line.

Concept: Graphing a linear relation with negative coordinates

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In one sentence

The question this lesson answers

How do we graph y equals 2x minus 3, when some of the numbers are negative?

A relation is a rule that links x and y. This one says: double x, then subtract 3.

Transcript

What the lesson says

How do we graph y equals 2x minus 3, when some of the numbers are negative?

A relation is a rule that links x and y. This one says: double x, then subtract 3.

Make a table of values, which pairs each x with its y. Use x from negative 2 to 3.

Put negative 2 in place of x. Double it to get negative 4, then subtract 3 to get negative 7.

Negative 1 doubled is negative 2, and negative 2 minus 3 is negative 5.

0 doubled is 0, and 0 minus 3 is negative 3.

1 doubled is 2, and 2 minus 3 is negative 1.

2 doubled is 4, and 4 minus 3 is 1.

3 doubled is 6, and 6 minus 3 is 3.

Each row is an ordered pair: first the x-coordinate, then the y-coordinate.

The x-axis goes across, and the y-axis goes up and down. They cross at the origin, 0, 0.

Start at the origin. Negative 2 means go left 2, and negative 7 means go down 7.

For negative 1, negative 5, go left 1, then down 5.

The same way, plot 0, negative 3 on the y-axis, then 1, negative 1, then 2, 1, and 3, 3.

A dashed line through them shows that all six points line up, so the relation is linear.

Watch the signs. Dropping them turns negative 1, negative 5 into 1, 5, which is far off the line.

And keep x first. Swapping them gives negative 5, negative 1, which is off the line too.

So, to graph a relation: make a table of values, plot each ordered pair, and check that the points line up.

Curriculum

Where this fits

British Columbia, Grade 8

Mathematics, Patterns and algebra: discrete linear relations (extended to larger numbers, limited to integers)BC8-MA-18

Previous: Choosing a Scale When the Numbers Are LargeNext: One Relation, Three Ways: Expression, Table and Graph

The outcomes and strands follow the British Columbia curriculum.

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