Question

A line passes through the point (4, –6) and has a slope of Negative three-fourths. Which is the equation of the line?
y = negative three-fourths x minus 3
y = negative three-fourths x minus 6
y = negative 3 x minus three-fourths
y = negative 6 x minus three-fourths

Answer 1

To find the equation of a line given a point and a slope, you can use the point-slope form of a line's equation:

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

where \( (x_1, y_1) \) is the given point and \( m \) is the slope.

In this case, the point is \( (4, -6) \) and the slope \( m \) is \(-\frac{3}{4}\).

Plugging these values into the point-slope equation:

\[
y - (-6) = -\frac{3}{4}(x - 4)
\]

This simplifies to:

\[
y + 6 = -\frac{3}{4}(x - 4)
\]

Distributing \(-\frac{3}{4}\):

\[
y + 6 = -\frac{3}{4}x + 3
\]

Now, subtract 6 from both sides:

\[
y = -\frac{3}{4}x + 3 - 6
\]

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

None of your provided options exactly match this equation. The correct equation in standard terms would be:

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

so it seems like the closest would be:

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

If the options are required to be in a specific form, please let me know!