Question

The straight line ℓ is perpendicular to the line y + 2x = 9 and passes through the point p(4, 3). find the x-intercept of ℓ.

Answer 1

The slope of the line l is the opposite reciprocal of y+2x=9. Rearranged the equation to y=9-2x and we get a slope of -2. The opposite reciprocal of -2 is 1/2.

y-y=m(x-x)
y-3=.5(x-4)
y=.5x+1

At the x-intercept, y=0, so
0=.5x+1
-1=.5x
x=-2