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

The equation of a line can be written in point-slope form:

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

where \((x_1, y_1)\) is a point on the line, and \(m\) is the slope. Given the point \((4, -2)\) and the slope \(m = -\frac{3}{4}\), we substitute these into the equation:

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

Simplifying:

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

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

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

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

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

Thus, the equation of the line is:

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

Would you like further details or clarifications?

Here are 5 related questions you might explore:
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 slope given two points?
4. What is the meaning of the y-intercept in this context?
5. How do parallel and perpendicular lines relate in terms of slope?

**Tip:** The slope \(m\) in the equation \(y = mx + b\) represents the steepness of the line, and the sign indicates whether it rises or falls.

Learn how to find the equation of a line passing through the point (4, -2) with a slope of -3/4 using point-slope and slope-intercept forms. This step-by-step guide covers essential algebraic concepts suitable for students in Grades 8-10.

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