Question
Use the given conditions to write an equation for the line in the indicated form. Passing through \( (4,3) \) and perpendicular to the line whose equation is \( y= \) \( 8 x+7 \); point-slope form
Ask by Fitzgerald Mccoy. in the United States
Feb 25,2025
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Tutor-Verified Answer
Answer
The equation of the line in point-slope form is \( y - 3 = -\frac{1}{8}(x - 4) \).
Solution
The given line is y = 8x + 7, so its slope is 8. For a line to be perpendicular, its slope must be the negative reciprocal of 8, which is -1/8.
Using the point-slope form, where the point is (4,3), the equation is:
y - 3 = (-1/8)(x - 4)
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Simplify this solution Extra Insights
To find the equation of a line that passes through the point \( (4,3) \) and is perpendicular to the given line \( y = 8x + 7 \), we first need to determine the slope of the given line, which is \( 8 \). The slope of a line that is perpendicular to another is the negative reciprocal of the original line's slope. Therefore, the slope of the new line will be \( -\frac{1}{8} \). Now we can use the point-slope form of a line, which is expressed as \( y - y_1 = m(x - x_1) \). Substituting in the point \( (4, 3) \) and the slope \( -\frac{1}{8} \), we get: \[ y - 3 = -\frac{1}{8}(x - 4) \]
