To find the slope of the line that passes through the points [tex]\((2, 9)\)[/tex] and [tex]\((18, -3)\)[/tex], we can use the formula for the slope of a line that passes through two points, [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here, the coordinates of the two points are [tex]\((2, 9)\)[/tex] and [tex]\((18, -3)\)[/tex].
Let's substitute these coordinates into the formula:
1. Identify the coordinates:
- [tex]\(x_1 = 2\)[/tex]
- [tex]\(y_1 = 9\)[/tex]
- [tex]\(x_2 = 18\)[/tex]
- [tex]\(y_2 = -3\)[/tex]
2. Substitute the values into the slope formula:
[tex]\[
\text{slope} = \frac{-3 - 9}{18 - 2}
\][/tex]
3. Simplify the numerator and the denominator:
[tex]\[
\text{slope} = \frac{-12}{16}
\][/tex]
4. Simplify the fraction [tex]\(\frac{-12}{16}\)[/tex] to its simplest form. Both the numerator and denominator can be divided by 4:
[tex]\[
\text{slope} = \frac{-12 \div 4}{16 \div 4} = \frac{-3}{4}
\][/tex]
Therefore, the slope of the line that passes through the points [tex]\((2, 9)\)[/tex] and [tex]\((18, -3)\)[/tex] is [tex]\(-\frac{3}{4}\)[/tex], which is equivalent to [tex]\(-0.75\)[/tex] in decimal form.
So the correct answer is:
[tex]\[
\text{slope} = -0.75
\][/tex]
