Question

Write the slope intercept form of the equation of the line passing through (-4,6) and perpendicular to y=-2x-5.

Answer 1

`y=(1)/(2) x+8`

Explanation:

Hi there!

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)

1) Determine the slope (m)

Perpendicular lines will always have slopes that are negative reciprocals of each other. For example, two perpendicular lines might have slopes of 3 and -1/3.

After observing the equation y=-2x-5, we can conclude that the slope is -2. Therefore, a line perpendicular to this line 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 (-4,6)

`6=(1)/(2)(-4)+b\\6=-2+b`

Add 2 to both sides

`6+2=-2+b+2\\8=b`

Therefore, the y-intercept is 8. Plug this back into
`y=(1)/(2) x+b`:

`y=(1)/(2) x+8`

I hope this helps!