Question

1. how much money will you make for selling 30 tickets?
2. grid graph $y = 2x - 4$ using the slope and y-intercept. (lesson 6)
3. grid consider the equation $y = -3$. (lesson 6)

a. graph $y = -3$.
b. describe the graph of $y = -3$.

Explanation:

11. Grid Graph \( y = 2x - 4 \) using the slope and y - intercept

Step 1: Identify slope and y - intercept

The equation of a line in slope - intercept form is \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. For the equation \( y = 2x-4 \), we can see that the slope \( m = 2=\frac{2}{1}\) and the y - intercept \( b=- 4 \).

Step 2: Plot the y - intercept

The y - intercept is the point where the line crosses the y - axis. When \( x = 0 \), \( y=-4 \). So we plot the point \( (0,-4) \) on the coordinate grid.

Step 3: Use the slope to find another point

The slope \( m=\frac{\text{rise}}{\text{run}}=\frac{2}{1} \). Starting from the point \( (0,-4) \), we move up 2 units (because the rise is 2) and then 1 unit to the right (because the run is 1). This gives us the point \( (0 + 1,-4 + 2)=(1,-2) \). We can also move down 2 units and left 1 unit from \( (0,-4) \) to get another point \( (0-1,-4 - 2)=(-1,-6) \).

Step 4: Draw the line

Using a straightedge, we draw a line that passes through the points we have plotted (e.g., \( (0,-4) \), \( (1,-2) \), \( (-1,-6) \)). This line represents the graph of \( y = 2x-4 \).

12. Grid Consider the equation \( y=-3 \)

A. Graph \( y = - 3 \)

Step 1: Understand the equation

The equation \( y=-3 \) is a horizontal line. For any value of \( x \), the value of \( y \) is always - 3.

Step 2: Plot points

We can choose several values of \( x \) (e.g., \( x=-2 \), \( x = 0 \), \( x = 3 \)). When \( x=-2 \), \( y=-3 \), so the point is \( (-2,-3) \); when \( x = 0 \), \( y=-3 \), so the point is \( (0,-3) \); when \( x = 3 \), \( y=-3 \), so the point is \( (3,-3) \).

Step 3: Draw the line

Using a straightedge, we draw a horizontal line that passes through all the points \( (x,-3) \) for different values of \( x \). This line is parallel to the x - axis and passes through the y - axis at \( (0,-3) \).

B. Describe the graph of \( y=-3 \)

The equation \( y = - 3 \) represents a horizontal line. In the coordinate plane, a horizontal line has a slope of 0. It passes through all points where the y - coordinate is - 3, regardless of the value of the x - coordinate. So it is a horizontal line parallel to the x - axis and intersects the y - axis at \( (0,-3) \).

Answer:

The graph of \( y=-3 \) is a horizontal line (with a slope of 0) that passes through all points with a y - coordinate of - 3 (e.g., \( (-2,-3) \), \( (0,-3) \), \( (3,-3) \)) and is parallel to the x - axis.