Question
What is a point-slope equation of the line with slope -13 that goes through the point (5, 7)?
31-7 = -13(x- 5)
4+ 5=-13(x +7)
01-5--130-71
31-7 = -13(x- 5)
4+ 5=-13(x +7)
01-5--130-71
Answers
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Answered by
GPT-4o mini
To create the point-slope equation of a line given a slope and a point, you can use the point-slope form of the equation:
\[
y - y_1 = m(x - x_1)
\]
where \(m\) is the slope, and \((x_1, y_1)\) is the point through which the line passes.
In this case, the slope \(m = -13\) and the point is \((5, 7)\), so \(x_1 = 5\) and \(y_1 = 7\).
Plugging these values into the equation:
\[
y - 7 = -13(x - 5)
\]
So the point-slope equation of the line is:
\[
y - 7 = -13(x - 5)
\]
You can simplify this further if needed, but this is the point-slope form of the line.
\[
y - y_1 = m(x - x_1)
\]
where \(m\) is the slope, and \((x_1, y_1)\) is the point through which the line passes.
In this case, the slope \(m = -13\) and the point is \((5, 7)\), so \(x_1 = 5\) and \(y_1 = 7\).
Plugging these values into the equation:
\[
y - 7 = -13(x - 5)
\]
So the point-slope equation of the line is:
\[
y - 7 = -13(x - 5)
\]
You can simplify this further if needed, but this is the point-slope form of the line.
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