Question

Which equation represents a line which is perpendicular to the line y=3/8x-1?A. 3x+8y=−40B. 3x-8y=-56C. 3y-8x=3D. 8x+3y=9

Answer 1

D. 8x + 3y = 9

Step-by-step explanation

The slopes of perpendicular lines are opposite reciprocals.

The slope of the given line is 3/8, so its opposite reciprocal is -8/3. From the options we have to find a line with this slope.

In the given line, it was easy to find the slope because the equation is in slope-intercept form, but in the options the equations are in standard form,

`ax+by=c`

If we solve this for y we get the slope-intercept form,

`by=-ax+c`
`y=-(a)/(b)x+(c)/(b)`

Thus the slope of a line whose equation is in standard form is,

`m=-(a)/(b)`

• Option A: a = 3, b = 8. The slope is -3/8 → ,not perpendicular

,

• Option B: a = 3, b = -8. The slope is 3/8 → ,not perpendicular

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• Option C: a = -8, b = 3. The slope is 8/3 → ,not perpendicular

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• Option D,: a = 8, b = 3. The slope is -8/3 → ,this line is perpendicular, to the given line