Question

Which of the following options would be the equation of a line perpendicular to the line y=−3x+5 ?(1 point)
Responses

y=3x+9
y equals 3 x plus 9

y=−1/3x+9
y equals negative Start Fraction 1 over 3 End Fraction x plus 9

y=−3x+9
y equals negative 3 x plus 9

y=1/3x+9

Answer 1

To find the equation of a line that is perpendicular to the line given by the equation \(y = -3x + 5\), we first need to determine the slope of the original line. The slope of the line \(y = -3x + 5\) is \(-3\).

Lines that are perpendicular to each other have slopes that are negative reciprocals. The negative reciprocal of \(-3\) is \(\frac{1}{3}\).

Now we can examine the provided options to find which equation has a slope of \(\frac{1}{3}\):

1. \(y = 3x + 9\) (slope = 3)
2. \(y = -\frac{1}{3}x + 9\) (slope = -\frac{1}{3})
3. \(y = -3x + 9\) (slope = -3)
4. \(y = \frac{1}{3}x + 9\) (slope = \frac{1}{3})

The correct choice is:

**y = \frac{1}{3}x + 9**

This line has the slope of \(\frac{1}{3}\), which is perpendicular to the slope of \(-3\).