Write an equation of the line that passes through $\left(1,5\right)$ and is perpendicular to the line shown. An equation of the perpendicular line is $y=$

Answer 1

find the equation of a line perpendicular to 2x+2y=-2 that passes through the point (9,8)

To find the slope of the line, rewrite this equation in slope-intercept form (y=mx+b)

2x + 2y = -2

x + y = -1 [divide all terms by 2]

y = -x-1 [subtract x from both sides]

The slope of this line is -1 (the coefficient in front of the x term).

The slope of the line perpendicular to this line is the negative reciprocal of the slope of this line, which is -(1/-1) = 1.

We have the slope of the perpendicular line and a point that it passes through. Plug these values into the point slope form equation of a line: y-y₁=m(x-x₁), where (x1, y1) is a point the line passes through, and m is the slope.

y-8 = 1(x-9)

y = x-1

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Answer 2

Perpendicular means the slope is the negative reciprocal = flipped and sign changed.

If the line given is y = 2x + 3, for example, the perpendicular line's slope will be -1/2.

Find the line with slope -1/2 that contains the point (1,5)

The line will be y = (-1/2)x + b

Plug in the point to find b.

5 = -1/2 * 1 + b

Add 1/2 to both sides.

1/2 = b

The equation of the line that's perpendicular to y = 2x + 3 and passes through the point (1,5) is y = (-1/2)x + 1/2