equation of a line that is perpendicular to the line `y=\frac{2}{3}x+5` and passes through the point `\left(4,1\right).`

Answer 1

The slope of the line y = (2/3) x + 5 is 2/3.

Any line perpendicular to that line has slope -1 / (2/3) = -3/2

Since (4,1) is a point on the perpendicular line, an equation of the line is y - 1 = -(3/2) (x - 4)

Simplifying, we get y = -(3/2)x + 7.