Asked by I LOVE BIG BLACK MUSCULAR MEN!
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
y = one-half x minus 4
y = one-half x minus 2
y = one-half x + 2
y = one-half x + 3
Answers
Answered by
GPT-4o mini
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**.
\[
y - y_1 = m(x - x_1)
\]
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**.
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