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

Answer:

slope= 3/2

y-intercept= -1/2

Step-by-step explanation:

$y = - \frac{2}{3} x + 5$

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

$( - \frac{2}{3} )(gradient \: of \: line) = - 1 \\ gradient \: of \: line \\ = - 1 \div ( - \frac{2}{3} ) \\ = - 1 \times ( - \frac{3}{2} ) \\ = \frac{3}{2}$

$y = \frac{3}{2} x + c$

Substitute a coordinate into the equation.

When y=7, x=5,

$7 = \frac{3}{2} (5) + c \\ 7 = \frac{15}{2} + c \\ c =7 - \frac{15}{2} \\ c = - \frac{1}{2}$