To find the equation of a line given a point and a slope, we use the point-slope form of a linear equation:

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

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

### Given:
- Point: \((3, -5)\)
- Slope: \(m = -\frac{3}{4}\)

### Solution:
Substitute the given values into the point-slope form:

\[
y - (-5) = -\frac{3}{4}(x - 3)
\]

Simplify this:

\[
y + 5 = -\frac{3}{4}(x - 3)
\]

Now, distribute \(-\frac{3}{4}\):

\[
y + 5 = -\frac{3}{4}x + \frac{9}{4}
\]

To get it in slope-intercept form (\(y = mx + b\)), subtract 5 from both sides:

\[
y = -\frac{3}{4}x + \frac{9}{4} - 5
\]

Convert \(-5\) to a fraction with a common denominator of 4:

\[
y = -\frac{3}{4}x + \frac{9}{4} - \frac{20}{4}
\]

Combine the fractions:

\[
y = -\frac{3}{4}x - \frac{11}{4}
\]

### Final Answer:
The equation of the line in slope-intercept form is:

\[
y = -\frac{3}{4}x - \frac{11}{4}
\]

Would you like a more detailed explanation or have any questions?

Here are 5 related questions you might find helpful:
1. How do you convert point-slope form to slope-intercept form?
2. What is the general form of a linear equation?
3. How do you find the y-intercept given a point and a slope?
4. What is the significance of the slope in a linear equation?
5. How can you graph a line given its equation in slope-intercept form?

**Tip:** When converting between forms of linear equations, always ensure you simplify fractions and combine like terms for a clean final equation.

Learn how to find the equation of a line through the point (3, -5) with a slope of -3/4. This problem involves using the point-slope form and converting it into slope-intercept form for the final answer. Suitable for students in Grades 8-10.

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