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Chapter 4: Q. 4.133 (page 535)

Find an equation of a line that is perpendicular to the line x=4that contains the point (4,鈭�5). Write the equation in slope-intercept form.

Short Answer

Expert verified

The equation of the line that is perpendicular to the linex=4isy=0x-5.

Step by step solution

01

Step 1. Given data

The given equation of the line is x=4

The point through which the line passes (4,-5)

02

Step 2. Equation of the perpendicular line

To find the equation we have the point-slope formula, that isy鈭�y1=m(x鈭�x1)

Here we have to find the slope to use this formula.

So as we know the new line will be perpendicular to x=4. Since this line is vertical, its perpendicular will be horizontal. Therefore the slope,m=0

Therefore, substituting the given point and slope in the point-slope formula we get,

y-(-5)=0(x-4)y+5=0y=-5

Thus the equation of the perpendicular line isy=-5

The slope-intercept formula is y=mx+b

Therefore, the equation in the slope-intercept form isy=0x-5

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