What is the equation of a line that passes through the point (8, 1) and is perpendicular to the line whose equation is y=−2/3x+5y=−2/3x+5 ?

Y = -2/3x + 5the slope here is -2/3. A perpendicular line will have a negative reciprocal slope. To find the negative reciprocal, we flip the slope and change the sign. So our perpendicular line will have a slope of 3/2 (see how I flipped -2/3 making it -3/2and then changed the sign, making it 3/2)

y = mx + b
slope(m) = 3/2
(8,1)x = 8 and y = 1
now we sub and find b, the y int
1 = 3/2(8) + b
1 = 12 + b
1 - 12 = b
-11 = b

so ur perpendicular equation is : y = 3/2x - 11 <==