Question

In the xy coordinate plane the slope of line p is 1 2 and its x-intercept is -3. Find the equation of a line that is perpendicular to p and intersects p at is x-intercept. A) y = -2x - 3 B) y = -2x + 3 C) y = -2x - 6 D) y = -2x + 6

Answer 1

Option C) y = -2x - 6

Explanation:

The correct question is

In the xy coordinate plane the slope of line p is 1/2 and its x-intercept is -3. Find the equation of a line that is perpendicular to p and intersects p at is x-intercept.

step 1

Find the slope of a line that is perpendicular to p

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of the slopes is equal to -1)

`m_1*m_2=-1`

we have

`m_1=(1)/(2)` ----> slope of line p

substitute

`((1)/(2))*m_2=-1`

`m_2=-2` ----> slope of the line perpendicular to p

step 2

Find the equation of the line that is perpendicular to p and intersects p at is x-intercept

we have

`m=-2`

`point\ (-3,0)`

Find the equation of the line in point slope form

`y-y1=m(x-x1)`

substitute

`y-0=-2(x+3)`

`y=-2x-6`