Lines: Parallel and Perpendicular Quiz

• 5

• 3

• -3

• 0

Answer explanation

The slope of a line in the equation y = mx + b is represented by 'm'. In this case, the equation is y = 3x + 5, where the slope (m) is 3. Therefore, the correct answer is 3.

• -2

• 4

• -4

• 2

Answer explanation

The y-intercept of a line in the form y = mx + b is the value of y when x = 0. In the equation y = -2x + 4, when x = 0, y = 4. Therefore, the y-intercept is 4.

Write the equation of a line in slope-intercept form with a slope of 2 and a y-intercept of -3.

Answer explanation

The slope-intercept form of a line is given by y = mx + b, where m is the slope and b is the y-intercept. Here, the slope is 2 and the y-intercept is -3, resulting in the equation y = 2x - 3, which is the correct choice.

• 2

• -2

• 0

Answer explanation

The slope of a line in the form y = mx + b is given by m. For the line y = \frac{1}{2}x + 7, the slope is \frac{1}{2}. Lines that are parallel have the same slope, so the slope of a parallel line is also \frac{1}{2}.

Answer explanation

The slope of the given line is -\frac{3}{4}. The slope of a line perpendicular to it is the negative reciprocal, which is \frac{4}{3}. Thus, the correct answer is \frac{4}{3}.

If a line has a slope of 0, what is the equation of the line that passes through the point (4, 5)?

Answer explanation

A line with a slope of 0 is horizontal. Since it passes through the point (4, 5), the y-coordinate remains constant at 5. Therefore, the equation of the line is y = 5.

• 7

• 0

• -7

• 1

Answer explanation

The y-intercept of a line in the form y = mx + b is the value of b when x = 0. In the equation y = 7x + 0, the y-intercept is 0, which is the correct answer.

Answer explanation

The slope of the given line is -1/3. A parallel line has the same slope. Using the point (3, 2) in the point-slope form, we find the y-intercept: y - 2 = -1/3(x - 3) leads to y = -1/3x + 4.

Answer explanation

The slope of the given line is 2. A line perpendicular to it has a slope of -1/2. Using the point-slope form with point (0,0), the equation is y = -1/2 x, which matches the correct choice.

• 4

• -4

• 0

Answer explanation

The slope of a line in the form y = mx + b is given by m. For the line y = -4x + 9, the slope is -4. Lines that are parallel have the same slope, so the slope of a line parallel to this one is also -4.