To write an equation in point-slope form, you need a point on the line and the slope of the line. The general formula for point-slope form is:

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

Where:

• $(x_1, y_1)$ is a point on the line
• $m$ is the slope of the line

Steps to use point-slope form with one point:

1. Identify the point $(x_1, y_1)$: The coordinates of the given point are used in the formula.
2. Find the slope $m$: If the slope is provided, you can directly substitute it into the formula. If not, you may need to calculate the slope using another point on the line.
3. Plug the point and slope into the formula: Substitute the values into the equation $y - y_1 = m(x - x_1)$.
4. Simplify (optional): If required, you can simplify or rearrange the equation into slope-intercept form ($y = mx + b$) or standard form.

Example:

Given the point $(2, 3)$ and slope $m = 4$: $y - 3 = 4(x - 2)$ This is the point-slope form of the line passing through $(2, 3)$ with a slope of 4.

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Would you like more details on how to find the slope, or practice using this form?

Here are 5 questions to explore further:

1. How do you find the slope when given two points?
2. How can you convert from point-slope form to slope-intercept form?
3. What is the significance of the slope in real-world applications?
4. How can you graph a line using point-slope form?
5. How do you handle vertical or horizontal lines in point-slope form?

Tip: Always double-check that you're using the correct signs when plugging in the point’s coordinates!