Use point-slope form to write the equation of a line that passes through the point (13,−8) with slope 3/2

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.

In this case:
- The point is \((13, -8)\), so \(x_1 = 13\) and \(y_1 = -8\).
- The slope is \(m = \frac{3}{2}\).

Substituting these values into the point-slope form equation:

\[
y - (-8) = \frac{3}{2}(x - 13)
\]

Simplifying the equation:

\[
y + 8 = \frac{3}{2}(x - 13)
\]

You can leave the equation in this form, or further simplify it into slope-intercept form by distributing the \(\frac{3}{2}\) and solving for \(y\):

\[
y + 8 = \frac{3}{2}x - \frac{39}{2}
\]

Now, subtract 8 from both sides to isolate \(y\):

\[
y = \frac{3}{2}x - \frac{39}{2} - 8
\]

Convert 8 to a fraction:

\[
y = \frac{3}{2}x - \frac{39}{2} - \frac{16}{2}
\]

Simplify:

\[
y = \frac{3}{2}x - \frac{55}{2}
\]

So, the equation of the line is:

\[
y = \frac{3}{2}x - \frac{55}{2}
\]

Would you like further clarification or details on any part of this? Here are some related questions to deepen your understanding:

1. What is the difference between point-slope form and slope-intercept form?
2. How do you convert a line equation from point-slope form to standard form?
3. How can you find the slope of a line between two given points?
4. How do you interpret the slope in real-world problems?
5. How do you find the equation of a line parallel or perpendicular to a given line?

**Tip:** Always check if simplifying a fraction or decimal form helps make the equation clearer or easier to work with.

Use point-slope form to write the equation of a line that passes through the point (13,−8) with slope 3/2.

Learn how to write the equation of a line in point-slope form passing through the point (13,−8) with a slope of 3/2. This detailed solution explains how to convert the equation to slope-intercept form. Ideal for students in Grades 8-10 studying algebra and linear equations.

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