Muhammad Arslan Shabbir

Muhammad Arslan Shabbir

Answered question

2022-08-13

Answer & Explanation

xleb123

xleb123

Skilled2023-05-24Added 181 answers

To find an equation of a line perpendicular to the graph of y=14x+5 and passing through the point (3,8), we need to determine two things: the slope of the perpendicular line and its y-intercept.
The given equation is in slope-intercept form y=mx+b, where m represents the slope of the line. Since the given line has a slope of 14, the perpendicular line will have a slope that is the negative reciprocal of 14.
The negative reciprocal of 14 is 41=4. Therefore, the perpendicular line has a slope of 4.
Now, using the point-slope form of a line, we can write the equation of the perpendicular line:
yy1=m(xx1)
where (x1,y1) represents the given point (3,8), and m is the slope of the perpendicular line (4).
Substituting the values into the equation:
y8=4(x(3))
Simplifying:
y8=4(x+3)
y8=4x12
To obtain the equation in slope-intercept form, we can isolate y on one side:
y=4x12+8
y=4x4
Therefore, the equation of the line perpendicular to y=14x+5 and passing through the point (3,8) is y=4x4.

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