For each of the following tables of values:
Plot the points on a number plane.
State whether the graph of the equation is linear.
y = x
| x | -1 | 0 | 1 | 2 |
|---|---|---|---|---|
| y | -1 | 0 | 1 | 2 |
y = 4 x
| x | -2 | -1 | 0 | 1 |
|---|---|---|---|---|
| y | -8 | -4 | 0 | 4 |
y = 2 x
| x | -2 | -1 | 0 | 1 |
|---|---|---|---|---|
| y | -4 | -2 | 0 | 2 |
y = - x
| x | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| y | 0 | -1 | -2 | -3 |
y = \dfrac{x}{5}
| x | -5 | 0 | 5 | 10 |
|---|---|---|---|---|
| y | -1 | 0 | 1 | 2 |
y = - \dfrac{x}{3}
| x | -3 | 0 | 3 | 6 |
|---|---|---|---|---|
| y | 1 | 0 | -1 | -2 |
For each of the following equations:
Construct a table of values for x=-1,0,1,2.
Plot the points from the table of values on a number plane.
Sketch the graph of the equation.
Consider the equation y = \dfrac{x}{2}.
Complete the table of values below:
| x | -6 | -4 | -2 | 0 |
|---|---|---|---|---|
| y |
Plot the points from the table on a number plane.
Sketch the graph of y = \dfrac{x}{2}.
Consider the equation y = - \dfrac{x}{5}.
Complete the table of values below:
| x | -10 | -5 | 0 | 5 |
|---|---|---|---|---|
| y |
Plot the points from the table on a number plane.
Sketch the graph of y = - \dfrac{x}{5}.
Consider the equation y = \dfrac{x}{2} + 5.
Complete the table of values below:
| x | -4 | -2 | 0 | 2 |
|---|---|---|---|---|
| y |
Plot the points from the table on a number plane.
Sketch the graph of y = \dfrac{x}{2} + 5.
Consider the equation y = - \dfrac{x}{4} + 5.
Complete the table of values below:
| x | -8 | -4 | 0 | 4 |
|---|---|---|---|---|
| y |
Plot the points from the table on a number plane.
Sketch the graph of y = - \dfrac{x}{4} + 5.
Consider the equation y =9x+1.
Complete the table of values below:
| x | -2 | -1 | 0 | 1 |
|---|---|---|---|---|
| y |
Plot the points from the table on a number plane.
Sketch the graph of y = 9x+1.
Consider the equation y =\dfrac{x}{6}-5.
Complete the table of values below:
| x | -5 | -3 | 0 | 6 |
|---|---|---|---|---|
| y |
Plot the points from the table on a number plane.
Sketch the graph of y =\dfrac{x}{6}-5.
Consider the equation y =-\dfrac{x}{3}-6.
Complete the table of values below:
| x | -3 | -2 | -1 | 0 |
|---|---|---|---|---|
| y |
Plot the points from the table on a number plane.
Sketch the graph of y =-\dfrac{x}{3}-6.
Let the height of a candle be y\text{ cm}. If the candle is lit, the height decreases according to the equation y = - 2 t + 8, where t is the elapsed time in minutes.
Complete the table of values below:
| t | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| y |
Sketch the graph of y = - 2 t + 8.
The height of candle and the time elapsed must be non-negative. For which values of t does the equation y = - 2 t + 8 accurately model the height of the candle?
Let the volume of water in a tank be V\text{ L}. If the tank is initially empty, then the amount of water in the tank is given by V = 5 t where t is the elapsed time in minutes and 5 is the rate that the tank fills in litres per minute.
Complete the table of values below:
| \text{Time }(t) | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| \text{Volume of water }(V) |
Sketch the graph of V = 5 t.
The volume of the tank is 15\text{ L} and the time elapsed is non-negative. For which values of t does the equation V = 5 t accurately model the volume of the tank?