Write an equation slope intercept form and standard form of a line passing through (1,4) and perpendicular to 2x=-3y+8

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.

y=3/2x+5/2.

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