What is the slope of the line that passes through the points left parenthesis, minus, 4, comma, 5, right parenthesis(−4,5) and left parenthesis, minus, 7, comma, 8, right parenthesis(−7,8)? Write your answer in simplest form.

To find the slope of the line that passes through the points \((-4, 5)\) and \((-7, 8)\), we use the slope formula:

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

Here, \((x_1, y_1)\) is \((-4, 5)\) and \((x_2, y_2)\) is \((-7, 8)\). Plugging in the coordinates:

\[
\text{slope} = \frac{8 - 5}{-7 - (-4)}
\]

Simplifying the expression:

\[
\text{slope} = \frac{3}{-7 + 4} = \frac{3}{-3} = -1
\]

So, the slope of the line is:

\[
\text{slope} = -1
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the slope of the line passing through the points (1, 2) and (3, 6)?
2. How do you interpret a slope of \(-1\) in the context of a line?
3. What is the slope of a horizontal line?
4. If a line has a slope of \(-1\), what is the angle of inclination with respect to the x-axis?
5. How do you find the slope of a line given its equation in standard form?

**Tip:** Remember that a negative slope indicates the line is decreasing as you move from left to right on a graph.

Learn how to find the slope of a line passing through the points (-4, 5) and (-7, 8) using the slope formula. This problem covers key concepts in coordinate geometry and slope calculation. Suitable for students in Grades 7-9.

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