Find the equation of the line through (4,-2) with slope -3/4.

To find the equation of a line, 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 (in this case, \( (4, -2) \)),
- \( m \) is the slope (in this case, \( -\frac{3}{4} \)).

Substituting the given values into the formula:

\[
y - (-2) = -\frac{3}{4}(x - 4)
\]

Simplify:

\[
y + 2 = -\frac{3}{4}(x - 4)
\]

Distribute the slope on the right-hand side:

\[
y + 2 = -\frac{3}{4}x + 3
\]

Now subtract 2 from both sides to isolate \( y \):

\[
y = -\frac{3}{4}x + 3 - 2
\]

\[
y = -\frac{3}{4}x + 1
\]

Thus, the equation of the line is:

\[
y = -\frac{3}{4}x + 1
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you convert point-slope form to slope-intercept form?
2. What is the general formula for a linear equation?
3. How can you find the slope between two points?
4. How would the equation change if the slope were positive?
5. What does the slope of a line represent in real-world problems?

**Tip:** The slope tells you how steep a line is and the direction it goes. Negative slopes mean the line decreases as \( x \) increases.

Learn how to find the equation of a line passing through the point (4, -2) with a slope of -3/4. This problem involves using the point-slope form and converting to the slope-intercept form. Suitable for students in Grades 8-10.

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