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

Question

Responses

y=13x+9
y equals Start Fraction 1 over 3 End Fraction x plus 9

y=−13x+9
y equals negative Start Fraction 1 over 3 End Fraction x plus 9

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

y=−3x+9

Answer 1

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

The slope of the line \( y = -3x + 5 \) is \(-3\). The negative reciprocal of \(-3\) is \(\frac{1}{3}\).

Now, let's check the options provided to see which one has a slope of \(\frac{1}{3}\):

1. \( y = \frac{1}{3}x + 9 \) (slope = \(\frac{1}{3}\)) - This is perpendicular.

2. \( y = -\frac{1}{3}x + 9 \) (slope = \(-\frac{1}{3}\)) - This is not perpendicular.

3. \( y = 3x + 9 \) (slope = \(3\)) - This is not perpendicular.

4. \( y = -3x + 9 \) (slope = \(-3\)) - This is not perpendicular.

Therefore, the equation of a line perpendicular to the line \( y = -3x + 5 \) is:

\( y = \frac{1}{3}x + 9 \).