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].
