Question
What is the point-slope form of the equation of the line that has a slope of 2 and passes through the point (−5,4)
?(1 point).
y−
=2
(x−
)
?(1 point).
y−
=2
(x−
)
Answers
GPT-4o mini
The point-slope form of the equation of a line is given by the formula:
\[
y - y_1 = m(x - x_1)
\]
where \(m\) is the slope, and \((x_1, y_1)\) is a point on the line.
For the line with slope \(m = 2\) that passes through the point \((-5, 4)\), we can substitute \(m\), \(x_1\), and \(y_1\) into the point-slope form:
1. \(m = 2\)
2. \(x_1 = -5\)
3. \(y_1 = 4\)
Plugging these values into the formula gives:
\[
y - 4 = 2(x - (-5))
\]
This can be simplified to:
\[
y - 4 = 2(x + 5)
\]
So, the point-slope form of the equation of the line is:
\[
y - 4 = 2(x + 5)
\]
In summary, in the format you provided, the answer is:
\[
y - 4 = 2(x + 5)
\]
\[
y - y_1 = m(x - x_1)
\]
where \(m\) is the slope, and \((x_1, y_1)\) is a point on the line.
For the line with slope \(m = 2\) that passes through the point \((-5, 4)\), we can substitute \(m\), \(x_1\), and \(y_1\) into the point-slope form:
1. \(m = 2\)
2. \(x_1 = -5\)
3. \(y_1 = 4\)
Plugging these values into the formula gives:
\[
y - 4 = 2(x - (-5))
\]
This can be simplified to:
\[
y - 4 = 2(x + 5)
\]
So, the point-slope form of the equation of the line is:
\[
y - 4 = 2(x + 5)
\]
In summary, in the format you provided, the answer is:
\[
y - 4 = 2(x + 5)
\]