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

Answer:

Option C) y = -2x - 6

Step-by-step 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

$m_1=\frac{1}{2}$ ----> slope of line p

substitute

$(\frac{1}{2})*m_2=-1$

$m_2=-2$ ----> 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

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

$y=-2x-6$