Question

Which is the slopc-intercept form of the

equation of a line that is perpendicular to
the line y = 2r – 7 and passes through the
point (-5, 6)?

Answer 1

`y=-(1)/(2) x+(7)/(2)`

Explanation:

Hi there!

What we need to know:

• Slope-intercept form:
  `y=mx+b` where m is the slope and b is the y-intercept (the value of y when x is 0)
• Perpendicular lines always have slopes that are negative reciprocals (ex. 2 and -1/2, 5/6 and -6/5, etc.)

1) Determine the slope (m)

`y=2r-7`

From the given equation, we can identify clearly that 2 is in the place of m, making it the slope. The negative reciprocal of 2 is -1/2, so therefore, the slope of a perpendicular line would be -1/2. Plug this into
`y=mx+b`:

`y=-(1)/(2) x+b`

2) Determine the y-intercept (b)

`y=-(1)/(2) x+b`

Plug in the given point (-5,6) and solve for b

`6=-(1)/(2) (-5)+b\\6=(5)/(2)+b`

Subtract 5/2 from both sides to isolate b

`6-(5)/(2)=(5)/(2)+b-(5)/(2)\\(7)/(2) =b`

Therefore, the y-intercept of the line is
`(7)/(2)`. Plug this back into
`y=-(1)/(2) x+b`:

`y=-(1)/(2) x+(7)/(2)`

I hope this helps!