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Kamila [148]
3 years ago
14

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

Mathematics
1 answer:
Paladinen [302]3 years ago
3 0

Answer <u>(assuming it is allowed to be in point-slope format)</u>:

y-4 = \frac{2}{3}(x-1)

Step-by-step explanation:

1) First, determine the slope. We know it has to be perpendicular to the given equation, y = -\frac{3}{2} x-4. That equation is already in slope-intercept form, or y = mx + b format, in which m represents the slope. Since -\frac{3}{2} 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 \frac{2}{3}.  

2) Now, use the point-slope formula, y-y_1 = m (x-x_1) to write the new equation with the given information. Substitute m, x_1, and y_1 for real values.

The m represents the slope, so substitute \frac{2}{3} in its place. The x_1 and y_1 represent the x and y values of a point the line intersects. Since the point crosses (1,4), substitute 1 for x_1 and 4 for y_1. This gives the following equation and answer:

y-4 = \frac{2}{3}(x-1)

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