Describe the relationship between x and y. Calculate y for the given x values. Draw a flow diagram and a table of values. Write the ordered pairs. Draw and plot the graph. Is the graph increasing or d

here is the solution for Question 1.

Question 1

1.1

a) The relationship describes a linear function where the output value ($y$) is obtained by multiplying the input value ($x$) by $-\frac{1}{3}$ and then adding 3.

b) To calculate the output values for each input value:

• For $x = 6$:

$$y = -\frac{1}{3}(6) + 3 = -2 + 3 = 1$$

• For $x = 3$:

$$y = -\frac{1}{3}(3) + 3 = -1 + 3 = 2$$

• For $x = 0$:

$$y = -\frac{1}{3}(0) + 3 = 0 + 3 = 3$$

• For $x = -3$:

$$y = -\frac{1}{3}(-3) + 3 = 1 + 3 = 4$$

• For $x = -6$:

$$y = -\frac{1}{3}(-6) + 3 = 2 + 3 = 5$$

The output values are $\boxed{1, 2, 3, 4, 5}$.

c) The completed flow diagram:

$$x \xrightarrow{\text{Multiply by } -\frac{1}{3}} \text{Result} \xrightarrow{\text{Add 3}} y$$

The input values are 6, 3, 0, -3, -6.
The corresponding output values are 1, 2, 3, 4, 5.

d) The table of input and output values:

x	6	3	0	-3	-6
y	1	2	3	4	5

e) The $x$ and $y$ values as ordered pairs:

$$\boxed{(6; 1), (3; 2), (0; 3), (-3; 4), (-6; 5)}$$

f) To draw and plot the graph, you would:

1. Draw a Cartesian plane with an x-axis and a y-axis.
2. Plot each of the ordered pairs from part (e) as points on the plane.
3. Draw a straight line connecting these points. This line represents the graph of the function $y = -\frac{1}{3}x + 3$.

g) The graph is decreasing. This is indicated by the negative coefficient of $x$ (the slope, $-\frac{1}{3}$). As the $x$ values increase, the $y$ values decrease.