What is the slope of the line that passes through the points left parenthesis, 7, comma, minus, 5, right parenthesis(7,−5) and left parenthesis, 16, comma, 7, right parenthesis(16,7)? Write your answer in simplest form.

To find the slope of the line that passes through the points \((7, -5)\) and \((16, 7)\), we can use the slope formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Where:
- \((x_1, y_1) = (7, -5)\)
- \((x_2, y_2) = (16, 7)\)

Substituting these values into the formula:

\[
m = \frac{7 - (-5)}{16 - 7} = \frac{7 + 5}{16 - 7} = \frac{12}{9}
\]

Next, simplify the fraction \(\frac{12}{9}\):

\[
m = \frac{12 \div 3}{9 \div 3} = \frac{4}{3}
\]

So, the slope of the line is \(\boxed{\frac{4}{3}}\).

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you interpret the slope of a line in a real-world context?
2. What is the significance of a positive versus negative slope?
3. How would you find the equation of the line given these two points?
4. How does the slope change if the points are swapped?
5. What does a slope of 0 or undefined indicate about a line?

**Tip:** Always check if the slope can be simplified by finding the greatest common divisor of the numerator and denominator.

Learn how to find the slope of a line passing through the points (7, -5) and (16, 7) using the slope formula. Detailed step-by-step solution provided. Suitable for Grades 7-9 students studying geometry and coordinate geometry.

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