To find the equation of the line that passes through the points [tex]\((15, 9)\)[/tex] and [tex]\((-2, 9)\)[/tex], follow these steps:
1. Identify the coordinates of the two points:
- Point 1: [tex]\((x_1, y_1) = (15, 9)\)[/tex]
- Point 2: [tex]\((x_2, y_2) = (-2, 9)\)[/tex]
2. Calculate the slope [tex]\(m\)[/tex] of the line:
The formula for the slope [tex]\(m\)[/tex] of a line passing through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Substituting the given values:
[tex]\[
m = \frac{9 - 9}{-2 - 15} = \frac{0}{-17} = 0
\][/tex]
Therefore, the slope [tex]\(m\)[/tex] is 0.
3. Write the equation of the line:
The general form of the equation of a line is:
[tex]\[
y = mx + b
\][/tex]
Since the slope [tex]\(m\)[/tex] is 0, the equation simplifies to:
[tex]\[
y = 0 \cdot x + b \implies y = b
\][/tex]
To find [tex]\(b\)[/tex], we use one of the given points. Since both points have the same [tex]\(y\)[/tex]-coordinate (9), we know that [tex]\(b = 9\)[/tex].
4. Conclusion:
Therefore, the equation of the line that passes through the points [tex]\((15, 9)\)[/tex] and [tex]\((-2, 9)\)[/tex] is:
[tex]\[
y = 9
\][/tex]
Thus, the correct choice from the given options is:
[tex]\[
y = 9
\][/tex]
