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=3x+9
y equals 3 x plus 9

y=−13x+9

Answer 1

To find the equation of a line that is perpendicular to the given line \( y = -3x + 5 \), we need to determine the slope of the given line. The slope-intercept form of the line is \( y = mx + b \), where \( m \) represents the slope.

For the line \( y = -3x + 5 \), the slope \( m \) is \( -3 \).

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

Therefore, a line that is perpendicular to \( y = -3x + 5 \) will have a slope of \( \frac{1}{3} \).

Among the options provided, the equation with this slope is:

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

So, the correct answer is:
**y = \(\frac{1}{3}\)x + 9**