Question

Find the slope and y-intercept of the line that is

perpendicular to y = -2/3x + 5 and passes
through the point (5, 7).

Answer 1

slope= 3/2

y-intercept= -1/2

Explanation:

`y = - (2)/(3) x + 5`

The product of the gradients of 2 perpendicular lines is -1.

`( - (2)/(3) )(gradient \: of \: line) = - 1 \\ gradient \: of \: line \\ = - 1 / ( - (2)/(3) ) \\ = - 1 * ( - (3)/(2) ) \\ = (3)/(2)`

`y = (3)/(2) x + c`

Substitute a coordinate into the equation.

When y=7, x=5,

`7 = (3)/(2) (5) + c \\ 7 = (15)/(2) + c \\ c =7 - (15)/(2) \\ c = - (1)/(2)`