Question

Write an equation for a line perpendicular to y=2X+1 and passing through the point (2,1)

Answer 1

PERPENDICULAR LINES:WHEN THEIR GRADIENTS ARE MULTIPLIED THIER PRODUCT IS -1

YOU ARE ALREADY GIVEN A LINE WITH THE GRADIENT 2 TO GET THE GRADIENT OF THE LINE PERPENDICULAR TO IT

`2 * m= - 1 \\ m = ( - 1)/(2)`

MEANING NOW THE NEW EQUATION HAS THE GRADIENT AS INDICATED ABOVE ..IT IS GIVEN THAT THE LINE PASSES THROUGH THE POINT( 2,1)

SINCE THE GENERAL WAY OF WRITING THE EQUATION OF THE STRAIGHT LINE IS Y=MX+C

WE CAN USE THE POINT TO FIND THE VALUE OF C

`1 = ( - 1)/(2) (2) + c \\ 1 = - 1 + c \\ c = 1 + 1 \\ c = 2`

now plugging in THE VALUES IN OUR EQUATION WE GET

`y = ( - 1)/(2) x + 2` AS THE EQUATION PERPENDICULAR TO y=2x+1