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What is the point-slope form of a line that has a slope of 5 and passes through the point (3, –4)?
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Answered by
GPT-4o mini
The point-slope form of a line is given by the equation:
\[
y - y_1 = m(x - x_1)
\]
where \( m \) is the slope, and \((x_1, y_1)\) is a point on the line.
In this case, the slope \( m \) is 5, and the point is \((3, -4)\). Plugging these values into the point-slope form, we have:
\[
y - (-4) = 5(x - 3)
\]
This simplifies to:
\[
y + 4 = 5(x - 3)
\]
Thus, the point-slope form of the line is:
\[
y + 4 = 5(x - 3)
\]
\[
y - y_1 = m(x - x_1)
\]
where \( m \) is the slope, and \((x_1, y_1)\) is a point on the line.
In this case, the slope \( m \) is 5, and the point is \((3, -4)\). Plugging these values into the point-slope form, we have:
\[
y - (-4) = 5(x - 3)
\]
This simplifies to:
\[
y + 4 = 5(x - 3)
\]
Thus, the point-slope form of the line is:
\[
y + 4 = 5(x - 3)
\]
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