The line perpendicular to y= (-3/2)x -4 and goes through (1,4)

Answer (assuming it is allowed to be in point-slope format):

Step-by-step explanation:

1) First, determine the slope. We know it has to be perpendicular to the given equation, . That equation is already in slope-intercept form, or y = mx + b format, in which m represents the slope. Since is in place of the m in the equation, that must be the slope of the given line.

Slopes that are perpendicular are opposite reciprocals of each other (they have different signs, and the denominators and numerators switch places). Thus, the slope of the new line must be .  

2) Now, use the point-slope formula, to write the new equation with the given information. Substitute , , and for real values.

The represents the slope, so substitute in its place. The and represent the x and y values of a point the line intersects. Since the point crosses (1,4), substitute 1 for and 4 for . This gives the following equation and

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