To solve the problem from the image, we need to find the equation of a line passing through the points (-1, 3) and (-9, 5). We will express the equation in point-slope form.

Steps:

1. Find the slope ($m$) of the line: The slope formula between two points $(x_1, y_1)$ and $(x_2, y_2)$ is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the given points $(-1, 3)$ and $(-9, 5)$: $m = \frac{5 - 3}{-9 - (-1)} = \frac{2}{-8} = -\frac{1}{4}$

2. Write the equation using the point-slope form: The point-slope form of the equation of a line is: $y - y_1 = m(x - x_1)$ You can use either point for $(x_1, y_1)$. Let's use the point $(-1, 3)$: $y - 3 = -\frac{1}{4}(x - (-1)) = -\frac{1}{4}(x + 1)$

Thus, the point-slope form of the line is: $y - 3 = -\frac{1}{4}(x + 1)$

This is the fully simplified point-slope form of the equation.

Let me know if you'd like further details, or if you have any questions!

5 Related Questions:

1. How do you convert point-slope form to slope-intercept form?
2. What does the slope tell you about the direction of the line?
3. How can you find the distance between two points on a line?
4. How do you find the midpoint of a line segment between two points?
5. What is the general form of a line equation, and how is it different from point-slope form?

Tip:

When working with the slope formula, be careful with signs; subtracting negatives can easily lead to mistakes!