Write an equation of the line that passes through the given point and has the given slope. (1, −5); slope −3/2

To write the equation of a line passing through a specific point \((x_1, y_1)\) with a given slope \(m\), you can use the **point-slope form** of a line:

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

Here, we have:
- Point: \((1, -5)\)
- Slope: \(m = -\frac{3}{2}\)

Substitute these values into the point-slope form:

\[
y - (-5) = -\frac{3}{2}(x - 1)
\]

Simplify the equation:

\[
y + 5 = -\frac{3}{2}(x - 1)
\]

Now, distribute the slope \(-\frac{3}{2}\) on the right side:

\[
y + 5 = -\frac{3}{2}x + \frac{3}{2}
\]

Finally, isolate \(y\) to get the equation in slope-intercept form \(y = mx + b\):

\[
y = -\frac{3}{2}x + \frac{3}{2} - 5
\]

Convert \(-5\) to a fraction with a denominator of 2:

\[
y = -\frac{3}{2}x + \frac{3}{2} - \frac{10}{2}
\]

Combine the constants:

\[
y = -\frac{3}{2}x - \frac{7}{2}
\]

So, the equation of the line is:

\[
y = -\frac{3}{2}x - \frac{7}{2}
\]

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Do you need more details or have any questions?

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1. How do we convert between point-slope and slope-intercept forms of a line?
2. What are the steps to find the y-intercept from point-slope form?
3. How do you calculate the slope given two points?
4. How would the equation change if the slope were positive?
5. What does a negative slope mean in terms of the line’s direction?

**Tip:** In point-slope form, directly substituting point coordinates and slope helps avoid errors when calculating the equation.

Write an equation of the line that passes through the given point and has the given slope. (1, −5); slope −3/2

Learn how to find the equation of a line passing through the point (1, -5) with a slope of -3/2. This solution uses point-slope form and simplifies it to slope-intercept form, covering essential algebraic concepts suitable for students in Grades 8-10.

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