To find the slope of the line that passes through the points (7, -5) and (16, 7), we use the slope formula:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Let's consider the given points where:
- Point 1: [tex]\((x_1, y_1) = (7, -5)\)[/tex]
- Point 2: [tex]\((x_2, y_2) = (16, 7)\)[/tex]
Now, substitute the coordinates into the formula:
[tex]\[ \text{slope} = \frac{7 - (-5)}{16 - 7} \][/tex]
Simplify the expressions inside the numerator and the denominator:
[tex]\[ \text{slope} = \frac{7 + 5}{16 - 7} \][/tex]
[tex]\[ \text{slope} = \frac{12}{9} \][/tex]
Finally, reduce the fraction to its simplest form by dividing both the numerator and the denominator by their greatest common divisor, which is 3:
[tex]\[ \text{slope} = \frac{12 \div 3}{9 \div 3} \][/tex]
[tex]\[ \text{slope} = \frac{4}{3} \][/tex]
So, the slope of the line that passes through the given points is [tex]\( \frac{4}{3} \)[/tex].
