What would be the equation of the line, which intercepts x-axis at -5 and is perpendicular to the line y = 2x + 3?

Let the line be $$l$$ which has x-intercept -5, => $$l$$ passes through (-5,0)

Slope of line $$ax + by + c = 0$$ is $$\frac{-a}{b}$$

=> Slope of line $$y = 2x + 3$$ => $$2x - y + 3 = 0$$

=> Slope = $$\frac{-2}{-1} = 2$$

Product of slopes of two perpendicular lines = -1

Let slope of line $$l$$ = $$m$$

=> $$m \times 2 = -1$$

=> $$m = \frac{-1}{2}$$

Now, equation of line having slope $$m$$ and passing through $$(x_1 , y_1)$$ is $$(y - y_1) = m(x - x_1)$$

=> $$(y - 0) = \frac{-1}{2} (x + 5)$$

=> $$2y = -x - 5$$

=> $$x + 2y = -5$$