Write an equation of the line perpendicular to the line y=-8/3x+2 and containing the point (32,6) write the answer in slope intercept form using integers or simplified fractions

Y = -8/3x + 2...slope here is -8/3. A perpendicular line will have a negative reciprocal slope. To find the negative reciprocal of the slope -8/3, u just flip the slope and change the sign. So our perpendicular line will have a slope of 3/8.

y = mx + b
slope(m) = 3/8
(32,6)...x = 32 and y = 6
now we sub and find b, the y int
6 = 3/8(32) + b
6 = 12 + b
6 - 12 = b
-6 = b

so ur perpendicular equation is : y = 3/8x - 6

For lines to be perpendicular to one another their slopes must be negative reciprocals of one another, mathematically:

m1*m2=-1

In this case:

-8m/3=-1

m=3/8, so far we have:

y=3x/8+b, solve for b with any point, we have (32, 6) so

6=3(32)/8+b

6=12+b

-6=b, so the line is:

y=3x/8-6  which is more neat in my opinion as:

y=(3x-48)/8 or even

y=3x/8-48/8