Question

Find the equation of the line that passes through (1,2) and is perpendicular to y=2x +3. Leave your answer in the form y=mx +c

Answer 1

y = -1/2x + 5/2.

Explanation:

If a line is perpendicular to another line, the slope of the line is the negative reciprocal of the other. In this case, the line is perpendicular to y = 2x + 3. That means the slope will be -1/2.

Now, we have y = -1/2x + c.

To solve for c, put in the points given.

2 = (-1/2) * 1 + c

c -1/2 = 2

c = 2 + 1/2

c = 4/2 + 1/2

c = 5/2

So, your final answer is that the equation of the line is y = -1/2x + 5/2.

Hope this helps!

Answer 2

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

Explanation:

Perpendicular => So, it would have a slope of negative reciprocal for this slope

Slope = m = -1/2

Now,

Point = (x,y) = (1,2)

So, x = 1, y = 2

Putting in the slope intercept equation to get c

=>
`y = mx+c`

=> 2 = (-1/2)(1) + c

=> 2+1/2 = c

=> c =
`(4+1)/(2)`

=> c =
`(5)/(2)`

Now, Putting m and c in the slope-intercept equation:

=>
`y = mx+c`

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