Question

Write an equation for a line that is perpendicular to the line given by x=9 and passes through the point (-6,-3)

Answer 1

y = -3

Explanation:

We are given an equation of the line, x=9.

And we want to write another equation of the line that is perpendicular to x=9 and passes through (-6, -3).

There are 3 ways to write the equation of the line:

• Slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept.
• Standard form, which is ax+by=c, where a, b, and c are integer coefficients, but a and b cannot be 0, while a also cannot be negative.
• Point-slope form, which is
  `y-y_1=m(x-x_1)`, where m is the slope and
  `(x_1,y_1)` is a point.

Any one of these forms would work, but let's use slope-intercept form, as it is the most common way to write the equation of the line.

Perpendicular lines have slopes that multiply to get -1. They are also considered negative and reciprocal. For example, 5 and -1/5 would be the slopes of perpendicular lines.

So, let's find the slope of x=9.

If a line is written like x=9, it means that when it is graphed, it will be a vertical line, and a vertical line has an undefined slope.

As you may know,
`(1)/(0)` is also considered to be undefined. This means that the slope of this vertical line can be written as
`(1)/(0)`.

Now, let's get the reciprocal of this slope (put the value of the numerator on the denominator and vice versa), then add a minus sign after it.

`(1)/(0)` =>
`-(0)/(1)` => 0

The slope of the line we're writing is 0.

We can replace m in y=mx+b with 0.

y = 0x + b

Now we need to find b.

As the equation passes through the point (-6,-3), we can use its values to help solve for b.

Substitute -6 as x and -3 as y in the equation.

-3 = 0(-6) + b

Multiply.

-3 = b

Replace b with -3 in the equation.

y = 0x - 3

This can also be written as:

y = -3