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 negative 3 x plus 9

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

Answer 1

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 \( m \) of the line \( y = -3x + 5 \) is -3.

The slope of a line that is perpendicular to another line is the negative reciprocal of the original slope. Thus, we take the reciprocal of -3, which is \(-\frac{1}{3}\), and then change the sign to get \(\frac{1}{3}\).

Now we look at the options provided to find the line with a slope of \(\frac{1}{3}\):

- **y = -3x + 9** (slope = -3)
- **y = \frac{1}{3}x + 9** (slope = \frac{1}{3})
- **y = -\frac{1}{3}x + 9** (slope = -\frac{1}{3})
- **y = 3x + 9** (slope = 3)

The equation of the line that is perpendicular to \( y = -3x + 5 \) is:

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