Question

3 ( y = -\frac{1}{3}x + 3 )
4 ( y = -120x + 600 )

Explanation:

Step1: Analyze the equation \( y = -\frac{1}{3}x + 3 \)

This is a linear equation in slope - intercept form \( y=mx + b \), where the slope \( m=-\frac{1}{3} \) and the y - intercept \( b = 3 \).
To graph the line, we first plot the y - intercept. The y - intercept is the point where \( x = 0 \), so when \( x = 0 \), \( y=3 \). So we plot the point \( (0,3) \).

Step2: Use the slope to find another point

The slope \( m=-\frac{1}{3}=\frac{\text{rise}}{\text{run}} \). The negative sign means we can go down 1 unit (since rise is - 1) and then run 3 units to the right (run is 3), or up 1 unit and run 3 units to the left.
Starting from the point \( (0,3) \), if we go down 1 unit ( \( y=3 - 1=2 \)) and run 3 units to the right ( \( x = 0+3 = 3 \)), we get the point \( (3,2) \).
We can also find the x - intercept by setting \( y = 0 \) in the equation \( 0=-\frac{1}{3}x + 3 \).
Solving for \( x \):

$$
LATEXBLOCK0
$$

So the x - intercept is \( (9,0) \).
Now we can draw a line through the points \( (0,3) \) and \( (9,0) \) (or \( (0,3) \) and \( (3,2) \)) on the given grid.

For the equation \( y=-120x + 600 \):

Step1: Analyze the equation \( y=-120x + 600 \)

This is also a linear equation in slope - intercept form \( y = mx + b \), where the slope \( m=-120 \) and the y - intercept \( b = 600 \).
The y - intercept is at \( (0,600) \). But since the grid is likely to have a smaller scale, we can find the x - intercept by setting \( y = 0 \).

Step2: Find the x - intercept

Set \( y = 0 \) in the equation \( 0=-120x+600 \).
Solving for \( x \):

$$
LATEXBLOCK1
$$

So the x - intercept is \( (5,0) \) and the y - intercept is \( (0,600) \). Since the slope is - 120 (a very steep negative slope), the line will be a very steep line going from \( (0,600) \) to \( (5,0) \) on the grid (considering the scale of the grid, we can use the two intercepts to draw the line).

Answer:

For \( y = -\frac{1}{3}x + 3 \), plot \( (0,3) \) and \( (9,0) \) (or other points using the slope) and draw a line. For \( y=-120x + 600 \), plot \( (0,600) \) and \( (5,0) \) and draw a line.