PRECALCULUS:GRAPHICAL,...-NASTA ED.
PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780134672090
Author: Demana
Publisher: PEARSON
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Chapter P, Problem 32RE
Solution

The equation of the line in slope-intercept form with given equation.

  y=52x+2

Given information:

The line passes through the point 2,−3 and is perpendicular to the line 2x+5y=3 .

Formula used:

  1. The equation of the lie in slope-intercept form that passes through a point x1,y1 with a slope m is given as: y=mx+c, where c can be find putting the point in the equation.
  2. The multiplication of slope of two perpendicular lines is equals to −1 .

Calculation:

To find the slope intercept form use the point-slope form of equation of line that passes through point 2,−3 , and is perpendicular to the line 2x+5y=3 , use the fact that the multiplication of slope of two perpendicular lines is equals to −1 .

First, find the slope of the line 2x+5y=3 by writing it’s equation in the form, y=mx+c , here m is slope, as

  2x+5y=35y=3−2xy=153−2xy=35−25xy=−25x+35

Comparing above equation with y=mx+c gives the slope of this equation,

  m=−25

Now find the slope of the line perpendicular to this line, since the the multiplication of slope of two perpendicular lines is equals to −1 , so the slope of the line, say m2 can be find as

  m×m2=−1−25×m2=−1m2=−1−25m2=52

Thus, the equation of the line can be written by using

  y=m2x+cy=52x+c

Now, since the line passes through the point 2,−3 putting it in place of x,y find c as

  −3=52−2+cc+−5=−3c=−3+5c=2c=−195

Thus, the slope intercept form of the line is

  y=52x+2

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Chapter P Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

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