Question

the equation of the line that is perpendicular to the line with equation y=-2x-1 and passes through the point (1, -2) is?

Answer 1

`y=(1)/(2) x-(5)/(2)`

Explanation:

Hi there!

Note that:

• 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 of each other (ex. 3 and -1/3, 5/6 and -6/5, etc.)

1) Determine the slope (m)

When we look at the given line,
`y=-2x-1`, we can identify that -2 is in the place of m, the slope of the line. Because perpendicular lines are negative reciprocals of each other, we know that a line perpendicular to this would have a slope of
`(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 (1,-2)

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

Subtract 1/2 from both sides

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

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

`y=(1)/(2) x-(5)/(2)`

I hope this helps!