Question
what equation of a line is perpendicular to the line y=−3x+5
Answers
GPT-4o mini
To find the equation of a line that is perpendicular to the given line \( y = -3x + 5 \), we first need to determine the slope of the given line. The equation is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope.
From the equation \( y = -3x + 5 \), we see that the slope \( m \) is \(-3\).
Perpendicular lines have slopes that are negative reciprocals of each other. Therefore, the slope of the perpendicular line will be:
\[
m_{\text{perpendicular}} = -\frac{1}{m} = -\frac{1}{-3} = \frac{1}{3}
\]
Now that we have the slope of the perpendicular line, we can use the point-slope form of the equation of a line:
\[
y - y_1 = m(x - x_1)
\]
where \( (x_1, y_1) \) is a point on the line. If you have a specific point through which the perpendicular line should pass, you can substitute that point into the equation.
However, if no specific point is provided, we can write a general equation for the line with slope \(\frac{1}{3}\):
\[
y - y_1 = \frac{1}{3}(x - x_1)
\]
This is the general form of the equation of a line that is perpendicular to the given line. If you need a specific line, please provide a point through which the line must pass.
From the equation \( y = -3x + 5 \), we see that the slope \( m \) is \(-3\).
Perpendicular lines have slopes that are negative reciprocals of each other. Therefore, the slope of the perpendicular line will be:
\[
m_{\text{perpendicular}} = -\frac{1}{m} = -\frac{1}{-3} = \frac{1}{3}
\]
Now that we have the slope of the perpendicular line, we can use the point-slope form of the equation of a line:
\[
y - y_1 = m(x - x_1)
\]
where \( (x_1, y_1) \) is a point on the line. If you have a specific point through which the perpendicular line should pass, you can substitute that point into the equation.
However, if no specific point is provided, we can write a general equation for the line with slope \(\frac{1}{3}\):
\[
y - y_1 = \frac{1}{3}(x - x_1)
\]
This is the general form of the equation of a line that is perpendicular to the given line. If you need a specific line, please provide a point through which the line must pass.