Question
What is the point slope form of the equation of the line that had a slope of 2 and passes through the point (-5,4)
Answers
GPT-4o mini
The point-slope form of a linear equation is given by the formula:
\[
y - y_1 = m(x - x_1)
\]
where \( m \) is the slope of the line, and \( (x_1, y_1) \) is a point on the line.
Given that the slope \( m = 2 \) and the point is \( (-5, 4) \) (where \( x_1 = -5 \) and \( y_1 = 4 \)), we can substitute these values into the point-slope formula:
\[
y - 4 = 2(x - (-5))
\]
This simplifies to:
\[
y - 4 = 2(x + 5)
\]
So, the point-slope form of the equation of the line is:
\[
y - 4 = 2(x + 5)
\]
\[
y - y_1 = m(x - x_1)
\]
where \( m \) is the slope of the line, and \( (x_1, y_1) \) is a point on the line.
Given that the slope \( m = 2 \) and the point is \( (-5, 4) \) (where \( x_1 = -5 \) and \( y_1 = 4 \)), we can substitute these values into the point-slope formula:
\[
y - 4 = 2(x - (-5))
\]
This simplifies to:
\[
y - 4 = 2(x + 5)
\]
So, the point-slope form of the equation of the line is:
\[
y - 4 = 2(x + 5)
\]