To find the equation of a line in point-slope form, we can use the formula:

$y - y_1 = m(x - x_1)$

Where:

• $(x_1, y_1)$ is a point on the line.
• $m$ is the slope of the line, which is given by the formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

We are given two points: $(3, -4)$ and $(1, 2)$.

Step 1: Calculate the slope ($m$).

$m = \frac{2 - (-4)}{1 - 3} = \frac{2 + 4}{1 - 3} = \frac{6}{-2} = -3$

Step 2: Use the point-slope form with one of the points.

Let's use $(3, -4)$:

$y - (-4) = -3(x - 3)$

Simplifying:

$y + 4 = -3(x - 3)$

This is the equation of the line in point-slope form. You can also use the point $(1, 2)$, and the result will be the same equation.

Would you like more details or have any questions?

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Here are five related questions to explore further:

1. How do you convert point-slope form to slope-intercept form?
2. What is the slope-intercept form of this line?
3. How do you find the equation of a line passing through one point with a given slope?
4. How do you determine if two lines are parallel?
5. How do you find the equation of a line that is perpendicular to this one?

Tip: Always double-check your slope calculation to avoid errors in the final equation.