Question

through: (3,-2), slope = - 4/3

Answer 1

To find the equation of a line given a point \((3, -2)\) and a slope of \(-\frac{4}{3}\), we can use the point-slope form of the equation of a line, which 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.

Plugging in the given point and slope:

- \(x_1 = 3\)
- \(y_1 = -2\)
- \(m = -\frac{4}{3}\)

Substituting these values into the point-slope form:

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

This simplifies to:

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

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

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

Now, isolate \(y\) by subtracting 2 from both sides:

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

This simplifies to:

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

Thus, the equation of the line is:

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