Middle Years

# 10.02 Visualising a table of values

Lesson

## Creating a table of values

A table of values, created using an equation, forms a set of points that can be plotted on a number plane. A line, drawn through the points, becomes the graph of the equation.

#### Exploration

We'll begin by creating a table of values for the following equation:

$y=3x-5$y=3x5

The first row of the table will contain values for the independent variable (in this case, $x$x). The choice of $x$x-values is often determined by the context, but in many cases they will be given. To find the corresponding $y$y-value, we substitute each $x$x-value into the equation $y=3x-5$y=3x5.

 $x$x $y$y $1$1 $2$2 $3$3 $4$4

Substituting $x=1$x=1:

 $y$y $=$= $3\times1-5$3×1−5 $=$= $3-5$3−5 $=$= $-2$−2

Substituting the remaining values of $x$x, allows us to complete the table:

 $x$x $y$y $1$1 $2$2 $3$3 $4$4 $-2$−2 $1$1 $4$4 $7$7

### Plotting points from a table of values

The $x$x and $y$y value in each column of the table can be grouped together to form the coordinates of a single point, $\left(x,y\right)$(x,y).

Each point can then be plotted on a coordinate plane.

Plotting points on a number plane

To plot a point, $\left(a,b\right)$(a,b), on a number plane, we first identify where $x=a$x=a lies along the $x$x-axis, and where $y=b$y=b lies along the $y$y axis.

For example, to plot the point $\left(3,4\right)$(3,4), we identify $x=3$x=3 on the $x$x-axis and construct a vertical line through this point. Then we identify $y=4$y=4 on the $y$y-axis and construct a horizontal line through this point. The point where the two lines meet has the coordinates $\left(3,4\right)$(3,4).

If we sketch a straight line through the points, we get the graph of $y=3x-5$y=3x5.

Notice that when sketching a straight line through a set of points, the line should not start and end at the points, but continue beyond them, across the entire coordinate plane.

Did you know?

To sketch a straight line graph we actually only need to identify two points!

• When checking if a set of points forms a linear relationship, we can choose any two of the points and draw a straight line through them. If the points form a linear relationship then any two points will result in a straight line passing through all the points.

#### Practice Questions

##### Question 1

Consider the equation $y=2x$y=2x.

1. Fill in the blanks to complete the table of values.

 $x$x $y$y $-1$−1 $0$0 $1$1 $2$2 $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
2. Plot the points in the table of values.

3. Is the relationship linear?

Yes, the relationship is linear.

A

No, the relationship is not linear.

B

Yes, the relationship is linear.

A

No, the relationship is not linear.

B

##### QUESTION 2

Consider the equation $y=4x+5$y=4x+5.

1. Fill in the blanks to complete the table of values.

 $x$x $y$y $-1$−1 $0$0 $1$1 $2$2 $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$

2. Plot the points that correspond to when $x=-1$x=1 and when $x=1$x=1:

3. Now, sketch the line that passes through these two points:

4. Does the point $\left(2,13\right)$(2,13) lie on this line?

Yes

A

No

B

Yes

A

No

B

##### Question 3

Consider the equation $y=-2x+4$y=2x+4.

1. Fill in the blanks to complete the table of values.

 $x$x $y$y $0$0 $1$1 $2$2 $3$3 $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$

2. Plot the points that correspond to when $x=0$x=0 and $y=0$y=0: