Question

What is the equation of the line perpendicular to y = -x+6 that passes through the

2
point (4, 1)?

Answer 1

`y=x-3`

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, 1/2 and -2, etc.)

1) Determine the slope (m)

`y = -x+6`

Looking at the given line, we can identify clearly that -1 is in the place of m, making it the slope of the line. Because perpendicular lines have slopes that are negative reciprocals of each other, we know that the slope of the line we're solving for is 1. Plug this into
`y=mx+b`:

`y=x+b`

2) Determine the y-intercept (b)

`y=x+b`

Plug in the given point (4,1)

`1=4+b`

Subtract 4 from both sides

`1-4=4+b-4\\-3=b`

Therefore, the y-intercept is -3. Plug this back into
`y=x+b`:

`y=x-3`

I hope this helps!