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A) Write an equation for a line in point-slope form that is parallel to the line y=2/3x-5 and passes through the point (3, 4).

b) Explain what would be different in part (a) if you were asked to write an equation for a line that is perpendicular instead of parallel.​

1 Answer

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Answer: a) y - 4 = 2/3(x) - 2

b) y - 4 = -3/2(x) -2

Explanation:

equation of original line: y = 2/3x -5

point on a line parallel to original line: (3,4)

The slope of a line parallel to a given line has the same slope, so the equation of the parallel line (in point-slope form) is:

(y - y1) = 2/3(x - x1)

point (x1, y1) is (3, 4)

plug (3,4) into the equation:

y - 4 = 2/3(x - 3)

y - 4 = 2/3(x) - 2

rewrite in slope-intercept form: y = 2/3(x) + 2

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the first line: - 1/m

Therefore, the slope of the perpendicular line = -3/2

Equation for the perpendicular line is:

y - 4 = -3/2(x) -2