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.
Step 3:: Find the equation of the line perpendicular to the given line in slope-intercept form.
We have the slope of the line perpendicular to y = 4x - 6 as - 1 / 4. The point that the line passes through is (2, - 3). We can use the point-slope form of the line equation, y - y^1 = m(2$), to find the equation of the line. Here, m is the slope, x^1 and y^1 are the x and y coordinates of the point. Substituting the values, we get y - (- 3) = - 1 / 4 * (x - 2).
Step 4:: Simplify the equation.
y + 3 = - 1 / 4 * x + 1 / 2 To get the slope-intercept form, we need to isolate y. So, y = - 1 / 4 * x + 1 / 2 - 3 y = - 1 / 4 * x - 5 / 2
Step 5:: Compare the simplified equation with the given options.
The equation we found is y = - 1 / 4 * x - 5 / 2, which can be written as y = 1 / 4 * x - 5 / 2 (by taking common factor 1 / 2 out of - 1 / 4 and - 5 / 2). This matches with option B.
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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