Asked by cesat
A line contains the point (-1,3) and has a slope of - 1/2. Write the equation for this line in point-slope form.
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Answered by
GPT-4o mini
To write the equation of a line in point-slope form, you can use the formula:
\[
y - y_1 = m(x - x_1)
\]
where \((x_1, y_1)\) is a point on the line and \(m\) is the slope.
In this case, the point is \((-1, 3)\) (where \(x_1 = -1\) and \(y_1 = 3\)), and the slope \(m\) is \(-\frac{1}{2}\).
Substituting these values into the point-slope formula:
\[
y - 3 = -\frac{1}{2}(x - (-1))
\]
This simplifies to:
\[
y - 3 = -\frac{1}{2}(x + 1)
\]
So the equation of the line in point-slope form is:
\[
y - 3 = -\frac{1}{2}(x + 1)
\]
\[
y - y_1 = m(x - x_1)
\]
where \((x_1, y_1)\) is a point on the line and \(m\) is the slope.
In this case, the point is \((-1, 3)\) (where \(x_1 = -1\) and \(y_1 = 3\)), and the slope \(m\) is \(-\frac{1}{2}\).
Substituting these values into the point-slope formula:
\[
y - 3 = -\frac{1}{2}(x - (-1))
\]
This simplifies to:
\[
y - 3 = -\frac{1}{2}(x + 1)
\]
So the equation of the line in point-slope form is:
\[
y - 3 = -\frac{1}{2}(x + 1)
\]
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