Question

Write the equation of the line that is perpendicular to y=2x-7 and passes through the point (6, 5)

A. y=2x-2
B.y= -1/2x+8
C.y=-1/2x-8
D.y=2x=2

Answer 1

B

Explanation:

we are given a equation of a line

we want to figure out the equation of the perpendicular line passes through the (6,5) points

in order to do so

recall that,

`\displaystyle m_{ \text{perpendicular}} = - (1)/(m)`

we got from our given equation that m=2

because equation of a line is y=mx+b

thus

`\displaystyle m_{ \text{perpendicular}} = - (1)/(2)`

remember that, when we want to figure out perpendicular line or parallel line we should the formula given by

`\displaystyle y - y_(1) = m(x - x_(1))`

since we got our perpendicular m is -½,
`x_1=6` and
`y_1=5`, substitute

`\displaystyle y - 5 = - (1)/(2) (x - 6)`

to get the perpendicular equation you should simplify the above equation to y=mx+b form

distribute -½:

`\displaystyle y - 5 = - (1)/(2) x + 3`

add 5 to both sides:

`\displaystyle y = - (1)/(2) x + 8`

hence,

our answer choice is B