KnowledgeMadeFun, home

Lesson · Grade 9 · Mathematics

Graphing y = ½x + 2 and Reading Between the Points

  • Grade 9
  • Mathematics
  • 2 min 2 s
  • British Columbia
  • BC9-MA-16

Using even x-values, a table of values gives five whole-number points for y = ½x + 2, which are plotted and joined with one straight line rather than left as dots. The line is then read at x = 1 to get y = 2.5 (interpolation), and the rule checks it: ½ × 1 + 2 = 2.5.

Concept: Graphing a linear relation with fraction and decimal values

Anyone can watch two lessons on the website without an account. Signing in is free, no payment and no card, and opens three a day; Plus has no limit.

Loading

Share to Google Classroom

In one sentence

The question this lesson answers

Let us graph y equals one half x plus 2. It is a linear relation: a rule linking x and y whose graph is a straight line.

Make a table of values: x-values in one column, their y-values in the other.

Transcript

What the lesson says

Let us graph y equals one half x plus 2. It is a linear relation: a rule linking x and y whose graph is a straight line.

Make a table of values: x-values in one column, their y-values in the other.

Half of an even number is an integer, so pick even x-values: negative 4, negative 2, 0, 2 and 4.

Substitute each x-value in place of x. For negative 4, half of negative 4 is negative 2, plus 2 is 0.

For negative 2, half of negative 2 is negative 1, plus 2 is 1.

For 0, half of 0 is 0, plus 2 is 2.

For 2, half of 2 is 1, plus 2 is 3.

For 4, half of 4 is 2, plus 2 is 4.

Each row is an ordered pair, x first, then y. From the origin, where the axes cross, go across to 2, then up to 3.

Plot the other rows the same way: negative 4, 0; negative 2, 1; 0, 2; and 4, 4.

A common mistake is to plot the points and stop there.

Every x-value in between has a y-value too, so join the points with one straight line.

Reading values between plotted points is called interpolation. Find y when x is 1.

Go up from 1 to the line, then across to the y-axis. It lands halfway between 2 and 3, at 2.5.

Check with the rule: half of 1 is 0.5, and 0.5 plus 2 is 2.5. It matches.

Plot easy points, draw a straight line through them, and read values in between.

Curriculum

Where this fits

British Columbia, Grade 9

Mathematics, Patterns and algebra: two-variable linear relations, using graphing, interpolation, and extrapolationBC9-MA-16

Previous: Discrete or Continuous: When to Join the PointsNext: Horizontal and vertical lines: y = 3 and x = −2

The outcomes and strands follow the British Columbia curriculum.

Keep going

More on this topic