Question

Write an equation of the line that passes through (0,9) and is perpendicular to the line y= -x+1

Answer 1

`y=x+9`

Explanation:

Hi there!

What we need to know:

• Linear equations are typically organized in slope-intercept form:
  `y=mx+b` where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)
• Perpendicular lines always have slopes that are negative reciprocals (ex. 3 and -1/3, 5/6 and -6/5, etc.)

1) Determine the slope (m)

`y=-x+1`

This equation can be written as
`y=-1x+1`. Now, we can identify clearly that -1 is the slope of this line. Because perpendicular lines have slopes that are negative reciprocals, we know that the slope of the line we're calculating for is
`-((1)/(-1) )`, or just 1.

Plug 1 into
`y=mx+b` as the slope:

`y=1x+b`

`y=x+b`

2) Determine the y-intercept (b)

Recall that the y-intercept is the value of y when the line crosses the y-axis. It occurs when x is equal to zero.

The given point is (0,9), meaning that y is 9 when x is 0. Therefore, the y-intercept is 9. Plug this into
`y=x+b`:

`y=x+9`

I hope this helps!