Listen to the instructions and identify the zero of the linear equation [tex]\(y - 6 = 3(x + 4)\)[/tex]. Then use the zero and another point to graph the line.

1. Identify the zero:
- What is the zero of the equation? Type your answer in the box.
- The zero of the graph is at the point _____.

2. Graph the equation [tex]\(y - 6 = 3(x + 4)\)[/tex]:
- To graph the line, click on the Point button to place the zero and another point on the graph.
- Do not use more than two points to graph the line. Additional points will be marked as incorrect.
- Next, click on the Line button, then click on the two points you placed on the graph. This will draw the line between the two points.



Answer :

To find the zero of the linear equation [tex]\( y - 6 = 3(x + 4) \)[/tex], follow these steps:

1. Set [tex]\( y \)[/tex] to zero:
[tex]\[ 0 - 6 = 3(x + 4) \][/tex]

2. Simplify the equation:
[tex]\[ -6 = 3(x + 4) \][/tex]

3. Solve for [tex]\( x \)[/tex]:
[tex]\[ -6 = 3x + 12 \][/tex]
[tex]\[ -6 - 12 = 3x \][/tex]
[tex]\[ -18 = 3x \][/tex]
[tex]\[ x = -6 \][/tex]

So, the zero of the equation is the point [tex]\((-6, 0)\)[/tex].

Next, to graph the line, we need another point on the line. Let's find the [tex]\( y \)[/tex]-value for [tex]\( x = 0 \)[/tex]:

1. Substitute [tex]\( x = 0 \)[/tex] into the original equation:
[tex]\[ y - 6 = 3(0 + 4) \][/tex]

2. Simplify the right side:
[tex]\[ y - 6 = 3 \cdot 4 \][/tex]
[tex]\[ y - 6 = 12 \][/tex]

3. Solve for [tex]\( y \)[/tex]:
[tex]\[ y = 12 + 6 \][/tex]
[tex]\[ y = 18 \][/tex]

So, another point on the line is [tex]\((0, 18)\)[/tex].

Summary:
The zero of the graph is at the point [tex]\((-6, 0)\)[/tex].

To graph the line [tex]\( y - 6 = 3(x + 4) \)[/tex]:

1. Plot the zero [tex]\((-6, 0)\)[/tex] on the graph.
2. Plot another point, which is [tex]\((0, 18)\)[/tex].
3. Draw a line through these two points.

By placing these points correctly on the graph and drawing the line through them, you will have the graph of the equation [tex]\( y - 6 = 3(x + 4) \)[/tex].

- The zero of the graph is at the point: [tex]\((-6, 0)\)[/tex].