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)
[tex]m_1*m_2=-1[/tex]
we have
[tex]m_1=\frac{1}{2}[/tex] ----> slope of line p
substitute
[tex](\frac{1}{2})*m_2=-1[/tex]
[tex]m_2=-2[/tex] ----> 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
[tex]m=-2[/tex]
[tex]point\ (-3,0)[/tex]
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
substitute
[tex]y-0=-2(x+3)[/tex]
[tex]y=-2x-6[/tex]
