Question

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

Answer 1

ANSWER:

Perpendicular means the slopes are negative-reciprocals.

So, the slope of the new line is the negative-reciprocal of 2 i.e, - 1/2.

Using point-slope,

y - 5 = - 1/2(x - 6)

y = - 1/2 x + 3 + 5

y = - 1/2x + 8.

So, Correct choice - [B] y = - 1/2x + 8.

Answer 2

Answer:

B

Step-by-step 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,

$\displaystyle m_{ \text{perpendicular}} = - \frac{1}{m}$

we got from our given equation that m=2

because equation of a line is y=mx+b

thus

$\displaystyle m_{ \text{perpendicular}} = - \frac{1}{2}$

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

$\displaystyle y - 5 = - \frac{1}{2} (x - 6)$

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

distribute -½:

$\displaystyle y - 5 = - \frac{1}{2} x + 3$

add 5 to both sides:

$\displaystyle y = - \frac{1}{2} x + 8$

hence,

our answer choice is B