Use point-slope form to write the equation of a line that passes through the point left parenthesis, 12, comma, 9, right parenthesis(12,9) with slope start fraction, 3, divided by, 5, end fraction 
5
3
​
 .

The **point-slope form** of the equation of a line is given by:

\[
y - y_1 = m(x - x_1)
\]

where \((x_1, y_1)\) is a point on the line, and \(m\) is the slope.

Here, the point \((x_1, y_1) = (12, 9)\), and the slope \(m = \frac{3}{5}\).

Substitute these values into the point-slope form:

\[
y - 9 = \frac{3}{5}(x - 12)
\]

This is the equation of the line in point-slope form.

If you'd like to convert it to slope-intercept form or get further details, let me know!

Here are some related questions to explore:
1. How do you convert from point-slope to slope-intercept form?
2. What is the significance of the slope in a line equation?
3. Can you use another point to verify the equation of this line?
4. How would the equation change if the slope were negative?
5. What are the advantages of using point-slope form over other forms?

**Tip:** Point-slope form is particularly useful when you know a point on the line and its slope!

Use point-slope form to write the equation of a line that passes through the point (12, 9) with slope 3/5.

Learn how to write the equation of a line in point-slope form that passes through the point (12, 9) with a slope of 3/5. This problem covers key algebra concepts, including using the point-slope form to describe linear equations. Suitable for Grades 8-10.

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