# In the xy coordinate plane the slope of line p is 1/2 and its x-intercept is -3. How do you find the equation of a perpendicular to p and intersects p at is x-intercept.?

Dec 29, 2016

$2 x + y + 6 = 0$

#### Explanation:

The equation of a line having a slope $m$ and passing through point $\left({x}_{1} , {y}_{1}\right)$ is $\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)$. As the slope of line is $\frac{1}{2}$ and its $x$-intercept is $- 3$ (i.e. it passes through $\left(- 3 , 0\right)$, its equation is

$\left(y - 0\right) = \frac{1}{2} \left(x - \left(- 3\right)\right)$ or $y = \frac{1}{2} x + \frac{3}{2}$ i.e. $x - 2 y + 3 = 0$.

As the slope of line $p$ is $\frac{1}{2}$, slope of line perpendicular to it is $\left(- 1\right) \div \frac{1}{2} = - 1 \times 2 = - 2$ and as it intersects $p$ at its $x$-intercept, it tpp passes through $\left(- 3 , 0\right)$ and its equation will be

$\left(y - 0\right) = - 2 \left(x - \left(- 3\right)\right)$ or $y = - 2 x - 6$ i.e. $2 x + y + 6 = 0$
graph{(x-2y+3)(2x+y+6)=0 [-13.96, 6.04, -4.16, 5.84]}