The equation of the line in the slope-intercept form is y=−2/3x+8/3.
The slope of the perpendicular line is negative inverse: m=3/2.
So, the equation of the perpendicular line is y=3/2x+a.
To find a, we use the fact that the line should pass through the given point: 4=(3/2)⋅(1)+a.
Thus, a=5/2.
Therefore, the equation of the line is y=3/2x+5/2.
Answer: y=3/2x+5/2.
