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Lesson · Grade 10 · Foundations of Mathematics and Pre Calculus

Writing the equation of a line from a table of values

  • Grade 10
  • Foundations of Mathematics and Pre Calculus
  • 2 min 15 s
  • British Columbia
  • BC10-MA-19

A table where y goes up 3 for each step of 1 in x, and y is 5 when x is 0, gives the slope and y-intercept of y = 3x + 5, and the graph shows the same 3 and 5. Going backwards from the equation to a table that starts at x = 2 shows why the first y-value is not always the y-intercept.

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In one sentence

The question this lesson answers

This table comes from a straight line. What is its equation?

We can write it in slope-intercept form: y equals m x plus b.

Transcript

What the lesson says

This table comes from a straight line. What is its equation?

We can write it in slope-intercept form: y equals m x plus b.

m is the slope, how steep the line is. b is the y-intercept, where the line crosses the y-axis.

Each step along the table, x goes up by 1.

And y goes up by 3 each step: 5 to 8, 8 to 11, and 11 to 14.

The slope is the change in y divided by the change in x: 3 divided by 1, which is 3.

The y-intercept is y when x is 0. Here x is 0 where y is 5, so b equals 5.

So the equation is y equals 3 x plus 5.

Check with x equals 2: 3 times 2 is 6, plus 5 is 11, which matches the table.

On a graph, the four points lie on one straight line.

It crosses the y-axis at 5: that is the y-intercept, b.

From each point to the next, it goes 1 across and 3 up: that is the slope, m.

Now go backwards, from the equation to a table: multiply each x by 3, then add 5.

x equals 2, 3, 4 and 5 give y equals 11, 14, 17 and 20.

Careful: this table does not start at x equals 0, so its first y value, 11, is not the y-intercept.

Step back to x equals 0, taking away 3 each step: 11 minus 3 is 8, and 8 minus 3 is 5.

So the y-intercept is still 5, and the equation is the same.

To recap: the slope is the change in y divided by the change in x, and the y-intercept is the value of y when x is 0.

Curriculum

Where this fits

British Columbia, Grade 10

Foundations of Mathematics and Pre Calculus 10, Linear relations: linear functions: slope and equations of linesBC10-MA-19

Previous: Horizontal and vertical lines: y = 3 and x = −2Next: Arithmetic sequences: first term and common difference

The outcomes and strands follow the British Columbia curriculum.

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