Question

Write the equation of a line that is perpendicular to the given line and that passes through the given point. y=2/3x+9;(-6,5)

Answer 1

Hay dear friend thank you for asking the question

according to the question we know that

y = mx +b

And given that y = 5 , m = -3/2, x = -6

so

5 = -3/2×(-6) +b

5 = 9 + b

-4 = b

now we can use our new slope and new intercept model equation then,

y = (-3/2)x-4

I hope it's help you

Answer 2

The perpendicular equation is y = -3/2x - 4.

You can find this by first realizing that perpendicular lines have opposite and reciprocal slopes. So since it starts at 2/3 we flip it and make it a negative and the new slope is -3/2. Now we can use that and the point to get the y intercept using slope intercept form.

y = mx + b

5 = (-3/2)(-6) + b

5 = 9 + b

-4 = b

And now we can use our new slope and new intercept to model the equation.

y = -3/2x - 4