Question

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Parallel & Perpendicular Lines Quick Check
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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=3x+9
y equals 3 x plus 9

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

y=−1/3x+9

Answer 1

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

1. Identify the slope of the original line:
The equation \( y = -3x + 5 \) has a slope of \( -3 \).

2. Find the negative reciprocal:
The negative reciprocal of \( -3 \) is \( \frac{1}{3} \).

Therefore, any line that is perpendicular to \( y = -3x + 5 \) will have a slope of \( \frac{1}{3} \). The equation of a line in slope-intercept form ( \( y = mx + b \) ) can take the form \( y = \frac{1}{3}x + b \), where \( b \) can be any value (like 9 in the options).

Among the provided options, the correct one is:
**\( y = \frac{1}{3}x + 9 \)** (this represents the line with slope \( \frac{1}{3} \) and a y-intercept of 9).

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