Which is the equation of a line that has a slope of One-half and passes through point (2, –3)?

Question

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.