Question

(4,-1) y=2x-4write an equation passing through the point and perpendicular to the given line

Answer 1

`\sf x +2y -2 = 0`

Explanation:

We need to write the equation of the line perpendicular to the given line and passing through the given point. The given equation is ,

`\sf \implies y = 2x - 4`

• The given equation is in slope intercept form , which is y = mx + c , comparing to which wr get ,

`\implies \sf m = 2`

• Now as we know that the product of slope of two perpendicular lines is -1 . Hence the slope of the perpendicular line will be ,

`\implies \sf m_(perp)= (-1)/(2)`

The given point to us is (4,-1) . So here we can use the point slope form of the line .

• The point slope form of the line is
  `\sf y-y_1 = m(x-x_1)` . On substituting the respective values ,

`\implies\sf y - y_1 = m(x - x_1) \\\\\sf \implies y - (-1) = (-1)/(2)( x - 4 ) \\\\\sf \implies 2 (y + 1 ) = -1(x - 4 ) \\\\\sf \implies 2y + 2 = -x + 4 \\\\\sf \implies x + 2y + 2 - 4 = 0 \\\\\sf \implies \boxed{\boxed{\pink{\sf x + 2y - 2 = 0 }}}`