To find the equation of a line that is perpendicular to the line given by \( y = -3x + 5 \), we first need to determine the slope of the original line. The slope-intercept form of a linear equation is \( y = mx + b \), where \( m \) is the slope.
In the equation \( y = -3x + 5 \), the slope \( m \) is \(-3\).
Lines that are perpendicular to each other have slopes that are negative reciprocals. Therefore, to find the slope of the line perpendicular to the given line, we take the negative reciprocal of \(-3\):
\[ \text{Slope of perpendicular line} = \frac{1}{3} \]
Now we can use this slope to write the equation of the line in slope-intercept form. The general form of the equation with the slope \( \frac{1}{3} \) is:
\[ y = \frac{1}{3}x + b \]
Where \( b \) is the y-intercept, which can be any real number. If you have a specific point through which this new line should pass, you can substitute that point into the equation to find the value of \( b \).
If the question provides specific options, they will typically be in a format such as \( y = \frac{1}{3}x + b \), and you can select the option that matches this form. Otherwise, any line with the slope \( \frac{1}{3} \) will be perpendicular to the original line.