QQuestionMathematics
QuestionMathematics
"Find the equation of the line perpendicular to y = 4x - 6 that passes through the point (2, - 3) in slope-intercept form.
A. y equals short dash 1 fourth x minus 5 over 2
B. y equals 1 fourth x minus 5 over 2
C. y equals 4 x minus 11
D. y equals short dash 4 x minus 11"
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Answer
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Step 1: Find the slope of the given line.
The equation of the given line is y = 4x - 6. Comparing this with the slope-intercept form y = mx + b, we can see that the slope (m) of the line is 4.
Step 2: Find the slope of the line perpendicular to the given line.
The slope of a line perpendicular to a given line with slope m is - 1 /m. So, the slope of the line perpendicular to y = 4x - 6 is - 1 / 4.
Final Answer
The equation of the line perpendicular to y = 4x - 6 that passes through the point (2, - 3) in slope-intercept form is y = 1 / 4 * x - 5 / 2 (option B).
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