Question

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

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=−3x+9
y equals negative 3 x plus 9

y=−13x+9

Answer 1

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

The slope of the given line \( y = -3x + 5 \) is \(-3\). The slope of a line that is perpendicular to another line is the negative reciprocal of the original line's slope.

The negative reciprocal of \(-3\) is:

\[
\frac{1}{3}
\]

Now, we can look for a line with this slope. The correct option should have a slope of \(\frac{1}{3}\).

Among the provided options, the one that matches this condition is:

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

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

\[
y = \frac{1}{3}x + 9
\]