(-6,8); perpendicular to y = -3/2x -1

Mathematics

1 answer:

UNO [17]3 years ago

7 0

Answer:

$y = \frac{2}{3} x + 12$

Step-by-step explanation:

$y = - \frac{3}{2} x - 1$

The gradient of a line is the coefficient of x when the equation of the line is written in the form of y=mx+c.

Thus, gradient of given line= $- \frac{3}{2}$ .

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

(Gradient of line)(-3/2)= -1

Gradient of line

$- 1 \div ( - \frac{3}{2} ) \\ = - 1( - \frac{2}{3} ) \\ = \frac{2}{3}$

Substitute m= $\frac{2}{3}$ into y=mx+c:

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

To find the value of c, substitute a pair of coordinates.

When x= -6, y= 8,

$8 = \frac{2}{3} ( - 6) + c \\ \\ 8 = - 4 + c \\ c = 8 + 4 \\ c = 12$

Thus, the equation of the line is $y = \frac{2}{3} x + 12$ .

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