Question

Write the equation of a line that is perpendicular to y=-1y=−1y, equals, minus, 1 and that passes through the point (8,-4)(8,−4)left parenthesis, 8, comma, minus, 4, right parenthesis.

Answer 1

Answer: y=-2

Explanation:

Lines with the form of x=cx=cx, equals, c are vertical lines, which means that their slopes are undefined. Lines perpendicular to vertical lines are horizontal lines, which have a slope of 000.

Since the given line is vertical, the slope of its perpendicular line is 000.

Hint #33 / 4

Step 2: Substitute the known point into linear equation

The perpendicular line will have a slope of \purpleC{0}0start color #aa87ff, 0, end color #aa87ff and pass through the point \redD{(-1,-2)}(−1,−2)start color #e84d39, left parenthesis, minus, 1, comma, minus, 2, right parenthesis, end color #e84d39. Let's start from the point-slope form of the equation of the perpendicular line, then solve for yyy. [What is the point-slope form?]

\begin{aligned} y-\redD{(-2)} &= \purpleC{0}(x-\redD{(-1)})\\\\\\ y+2 &= 0 \\\\\\ y &= \greenD{-2} \end{aligned}

y−(−2)

y+2

y

​

=0(x−(−1))

=0

=−2

​

Hint #44 / 4

Answer

y=\greenD{-2}y=−2y, equals, start color #1fab54, minus, 2, end color #1fab54.

Answer 2

x=8

Explanation:

The equation of line is y=mx+b where m is the slope

`y=-1`

The give equation is the equation of a horizontal line

for all horizontal line the slope is always 0

So the slope of y=-1 is 0

The perpendicular line of the given horizontal line is a vertical line

Slope of vertical line is undefined

equation of a vertical line is x= some number

The line passes through a point (8,-4)

The equation of the vertical line is x=8