Question

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.?

Answer 1

`2x+y+6=0`

Explanation:

The equation of a line having a slope `m` and passing through point `(x_1,y_1)` is `(y-y_1)=m(x-x_1)`. As the slope of line is `1/2` and its `x`-intercept is `-3` (i.e. it passes through `(-3,0)`, its equation is

`(y-0)=1/2(x-(-3))` or `y=1/2x+3/2` i.e. `x-2y+3=0`.

As the slope of line `p` is `1/2`, slope of line perpendicular to it is `(-1)-:1/2=-1xx2=-2` and as it intersects `p` at its `x`-intercept, it tpp passes through `(-3,0)` and its equation will be

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