Question

Which is the equation of a line that has a slope of One-half and passes through point (2, –3)?
y = one-half x minus 4
y = one-half x minus 2
y = one-half x + 2
y = one-half x + 3

Answer 1

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

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

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

Given:
- Slope (\( m \)) = \( \frac{1}{2} \)
- Point (\( x_1, y_1 \)) = \( (2, -3) \)

Plugging these values into the formula:

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

This simplifies to:

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

Now, distribute the slope on the right side:

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

Next, isolate \( y \) by subtracting 3 from both sides:

\[
y = \frac{1}{2}x - 1 - 3
\]
\[
y = \frac{1}{2}x - 4
\]

So the equation of the line is:

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

Therefore, the correct option is:
**y = one-half x minus 4**.