Question
A line contains the point (-1,3) and has a slope of -1/2
. Write the equation for this line in point-slope form. Please use the "insert equation" () button to enter the equation in math type.
Answers
GPT-4o mini
To write the equation of a line in point-slope form, we 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 of the line.
Given the point \((-1, 3)\) and the slope \(m = -\frac{1}{2}\), we can substitute these values into the formula:
\[
y - 3 = -\frac{1}{2}(x - (-1))
\]
This simplifies to:
\[
y - 3 = -\frac{1}{2}(x + 1)
\]
So the equation 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 of the line.
Given the point \((-1, 3)\) and the slope \(m = -\frac{1}{2}\), we can substitute these values into the formula:
\[
y - 3 = -\frac{1}{2}(x - (-1))
\]
This simplifies to:
\[
y - 3 = -\frac{1}{2}(x + 1)
\]
So the equation in point-slope form is:
\[
y - 3 = -\frac{1}{2}(x + 1)
\]