Question
Find point slope of (3,-4) and (2,-4). The slope is 0.
Answers
Answered by
GPT-4o mini
To find the point-slope form of a line given the points (3, -4) and (2, -4), we first confirm the calculation of the slope. The slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the given points (3, -4) and (2, -4):
\[
m = \frac{-4 - (-4)}{2 - 3} = \frac{0}{-1} = 0
\]
This confirms that the slope is indeed 0, which means the line is horizontal.
With a slope of 0 and using one of the points, say (3, -4), we can write the point-slope form of the line as follows:
Since the slope \(m\) is 0, the equation in point-slope form (though simplified here) can be represented generally as:
\[
y - y_1 = m(x - x_1)
\]
Substituting \(m = 0\), \(x_1 = 3\), and \(y_1 = -4\):
\[
y - (-4) = 0(x - 3)
\]
This simplifies to:
\[
y + 4 = 0
\]
or
\[
y = -4
\]
Thus, the equation of the line in slope-intercept form is \(y = -4\), which indicates a horizontal line passing through the point (3, -4) and (2, -4).
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the given points (3, -4) and (2, -4):
\[
m = \frac{-4 - (-4)}{2 - 3} = \frac{0}{-1} = 0
\]
This confirms that the slope is indeed 0, which means the line is horizontal.
With a slope of 0 and using one of the points, say (3, -4), we can write the point-slope form of the line as follows:
Since the slope \(m\) is 0, the equation in point-slope form (though simplified here) can be represented generally as:
\[
y - y_1 = m(x - x_1)
\]
Substituting \(m = 0\), \(x_1 = 3\), and \(y_1 = -4\):
\[
y - (-4) = 0(x - 3)
\]
This simplifies to:
\[
y + 4 = 0
\]
or
\[
y = -4
\]
Thus, the equation of the line in slope-intercept form is \(y = -4\), which indicates a horizontal line passing through the point (3, -4) and (2, -4).