Question

Tabitha is trying to find the equation of a line perpendicular to y = 1 over 2 x − 5 in slope-intercept form that passes through the point (2, −7). Which of the following equations will she use?

Answer 1

`y=-2x-3`

Explanation:

we know that

If two lines are perpendicular

then

the product of their slopes is equal to minus one

so

`m1*m2=-1`

Step 1

Find the slope of the given line

we have

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

the slope of the given line is equal to

`m1=(1)/(2)`

Step 2

Find the slope of the line perpendicular to the given line

`(1)/(2)*m2=-1`

`m2=-2`

Step 3

Find the equation of the line into slope intercept form

`y=mx+b`

we have

`m=-2`

`point(2,-7)`

substitute and solve for b

`-7=-2*(2)+b`

`-7=-4+b`

`b=-7+4=-3`

The equation of the line is equal to

`y=-2x-3`