Question

Which equation represents a line that has a slope of Negative one-half and passes through point (4, –5)?
y = negative one-half x + three-halves
y = negative one-half x + StartFraction 13 Over 2 EndFraction
y = negative one-half x minus 7
y = negative one-half x minus 3

Answer 1

To find the equation of the line with a slope \( m = -\frac{1}{2} \) that passes through the point \( (4, -5) \), we can use the point-slope form of the equation of a line:

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

Here, \( m = -\frac{1}{2} \), \( x_1 = 4 \), and \( y_1 = -5 \). Plugging in these values gives:

\[
y - (-5) = -\frac{1}{2}(x - 4)
\]

This simplifies to:

\[
y + 5 = -\frac{1}{2}(x - 4)
\]

Now, distribute on the right side:

\[
y + 5 = -\frac{1}{2}x + 2
\]

Next, isolate \( y \) by subtracting 5 from both sides:

\[
y = -\frac{1}{2}x + 2 - 5
\]

This simplifies to:

\[
y = -\frac{1}{2}x - 3
\]

So, the equation of the line is:

\[
y = -\frac{1}{2}x - 3
\]

The correct choice from your options is:

**y = negative one-half x minus 3.**