Parallel and Perpendicular Lines Quiz

Answer explanation

The slope of the given line is 3. A parallel line has the same slope. Using the point (1, 4) in the equation y = 3x + b, we find b = 7. Thus, the equation is y = 3x + 7.

Answer explanation

The slope of the given line is -2. The slope of a line perpendicular to it is the negative reciprocal, which is \frac{1}{2}. Using point-slope form with point (3, -1), we find the equation is \(y = \frac{1}{2}x - \frac{7}{2}\).

Answer explanation

The slope of the given line is -1/4. A parallel line has the same slope. Using point-slope form, y - 3 = -1/4(x + 2) simplifies to y = -1/4x + 11/2, matching the correct answer.

Answer explanation

The slope of the given line is \(\frac{3}{5}\). The slope of a line perpendicular to it is the negative reciprocal, \(-\frac{5}{3}\). Using the point-slope form with point \((0, 2)\), the equation is \(y = -\frac{5}{3}x + 2\).

Answer explanation

The slope of the given line is 7. A parallel line has the same slope. Using the point (2, -5) in the point-slope form, we find the equation: y + 5 = 7(x - 2) simplifies to y = 7x - 19.

Answer explanation

The slope of the given line is \(\frac{1}{2}\). The slope of a perpendicular line is the negative reciprocal, \(-2\). Using point-slope form with point \((4, 0)\), we find the equation is \(y = -2x + 8\).

Answer explanation

The slope of the given line is -3. A parallel line has the same slope. Using the point (5, -2), we can find the y-intercept: -2 = -3(5) + b, which gives b = -17. Thus, the equation is y = -3x - 17.

Answer explanation

The slope of the given line is 4. The slope of a perpendicular line is the negative reciprocal, which is -1/4. Using the point-slope form with point (-3, 5), we find the equation is y = -1/4x + 23/4.

Answer explanation

The slope of the given line is \(\frac{2}{3}\). A parallel line has the same slope. Using the point-slope form, we find the equation: \(y - 1 = \frac{2}{3}(x - 6)\), which simplifies to \(y = \frac{2}{3}x - 3\).

Answer explanation

The slope of the given line is -\frac{5}{2}. The slope of the perpendicular line is \frac{2}{5}. Using point-slope form with (2, -3), we find the equation is y = \frac{2}{5}x - \frac{19}{5}, which is the correct choice.