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Lesson · Grade 10 · Foundations of Mathematics and Pre Calculus

Slope-intercept form: graphing y = 2/3x − 1

  • Grade 10
  • Foundations of Mathematics and Pre Calculus
  • 2 min 9 s
  • British Columbia
  • BC10-MA-14

Starting from y = mx + b, the video graphs y = 2/3x − 1. It starts at b = −1 on the y-axis, then goes up 2 and right 3 to (3, 1) and (6, 3), checking each point and showing why (−1, 0) on the x-axis is a common mistake. It then reads the same line back off the graph (it crosses the y-axis at −1, and up 4 and right 6 gives m = 4/6 = 2/3) to write y = 2/3x − 1, and ends on a recap of what b and m mean.

Concept: Slope-intercept form: y = mx + b

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In one sentence

The question this lesson answers

Any line that is not vertical can be written as y equals m x plus b, called slope-intercept form.

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

Transcript

What the lesson says

Any line that is not vertical can be written as y equals m x plus b, called slope-intercept form.

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

Let us graph y equals two thirds x minus 1.

So m is two thirds and b is negative 1: the minus sign goes with b.

Step 1: start at b. On the y-axis, plot the point 0, negative 1.

Check: two thirds of 0 is 0, and 0 minus 1 is negative 1.

A common mistake is to start at negative 1 on the x-axis. That point is not on the line.

Step 2: slope is rise over run, so two thirds means up 2 and right 3.

From 0, negative 1, go up 2 and right 3, to the point 3, 1.

Check: two thirds of 3 is 2, and 2 minus 1 is 1.

Again, up 2 and right 3 takes you to the point 6, 3.

Check: two thirds of 6 is 4, and 4 minus 1 is 3.

Join the points with a straight line to finish the graph.

Now read the graph back. It crosses the y-axis at negative 1, so b is negative 1.

For the slope, use two points on grid corners, such as 0, negative 1 and 6, 3.

Between them it goes up 4 and right 6, so m is 4 over 6, which simplifies to two thirds.

That gives y equals two thirds x minus 1, the line we started with.

Recap: b is the y-intercept, where the line crosses the y-axis, and m is the slope, rise over run.

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-14

Previous: Four Kinds of Slope: Uphill, Downhill, Flat and a WallNext: Point-slope form: a line from one point and its slope

The outcomes and strands follow the British Columbia curriculum.

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