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Chapter 9: Q75. (page 535)

Which of the following is an equation for the line that passes through2,鈭�5 and is perpendicular to 2x+4y=8?

Ay=2x+10By=鈭�12x鈭�4Cy=2x鈭�9Dy=鈭�2x鈭�1

Short Answer

Expert verified

The equation for line passing through2,鈭�5 and perpendicular to2x+4y=8 is y=2x鈭�9.

Step by step solution

01

Step 1. Write equation in slope-intercept form.

Write an equation of line in slope-intercept form.

2x+4y鈭�2x=8鈭�2x4y4=8鈭�2x4y=鈭�12x+2

02

Step 2. Find slope of a line.

The slope of line with equationy=鈭�12x+2 is 鈭�12. The slope of perpendicular line is the opposite reciprocal of鈭�12 or 2.

03

Step 3. Find the y-intercept.

Substitute 2 for m and 2 for x and-5 for y in y=mx+c.

鈭�5=22+cc=鈭�5鈭�4=鈭�9

The equation in the form ofy=mx+c is y=2x鈭�9.

Therefore, option C is the required answer.

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