Slope and Line Relationships Quiz

What is the slope of a line that passes through the points (2, 3) and (6, 11)?

• 2

• 3

• 4

• 1/2

Answer explanation

To find the slope (m) between two points (x1, y1) and (x2, y2), use the formula m = (y2 - y1) / (x2 - x1). Here, m = (11 - 3) / (6 - 2) = 8 / 4 = 2. Thus, the slope is 2.

What is the slope of the line y = -3x + 5?

• -3

• 3

• 5

• -5

Answer explanation

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

Which equation represents a line with slope 4 and y-intercept -2?

• y = 4x - 2

• y = -2x + 4

• y = 4x + 2

• y = -4x - 2

Answer explanation

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Here, the slope is 4 and the y-intercept is -2, so the correct equation is y = 4x - 2.

Two lines are parallel if they have:

• The same y-intercept

• The same slope

• Opposite slopes

• Slopes that are negative reciprocals

Answer explanation

Two lines are parallel if they have the same slope. This means they rise and run at the same rate, ensuring they never intersect. The other options describe different relationships between lines.

What is the slope of a horizontal line?

• 1

• -1

• 0

• Undefined

Answer explanation

The slope of a horizontal line is 0 because there is no vertical change as you move along the line. This means the rise over run (change in y over change in x) equals zero, making the correct answer 0.

Find the slope of the line 2x + 3y = 12.

• 2/3

• -2/3

• 3/2

• -3/2

Answer explanation

To find the slope, rewrite the equation in slope-intercept form (y = mx + b). Starting with 2x + 3y = 12, isolate y: 3y = -2x + 12, then y = -2/3x + 4. The slope (m) is -2/3, making the correct answer -2/3.

Which line is parallel to y = (1/2)x - 3?

• y = 2x + 1

• y = (1/2)x + 5

• y = -2x - 3

• y = -(1/2)x + 7

Answer explanation

Lines are parallel if they have the same slope. The slope of y = (1/2)x - 3 is 1/2. The only line with the same slope is y = (1/2)x + 5, making it the correct choice.

If a line has slope 3/4, what is the slope of a line perpendicular to it?

• 3/4

• -3/4

• 4/3

• -4/3

Answer explanation

The slope of a line perpendicular to another is the negative reciprocal of the original slope. For a slope of 3/4, the negative reciprocal is -4/3.

What is the slope of the line passing through (-1, 4) and (3, -2)?

• 2/3

• -2/3

• 3/2

• -3/2

Answer explanation

To find the slope (m) between two points (x1, y1) and (x2, y2), use the formula m = (y2 - y1) / (x2 - x1). Here, m = (-2 - 4) / (3 - (-1)) = -6 / 4 = -3/2. Thus, the slope is -3/2.

Which equation represents a line perpendicular to 2x - 5y = 10?

• y = (2/5)x + 3

• y = -(5/2)x - 1

• y = (5/2)x + 4

• y = -(2/5)x + 2

Answer explanation

To find a line perpendicular to 2x - 5y = 10, we first find its slope, which is 2/5. The negative reciprocal is -5/2. The equation y = -(5/2)x - 1 has this slope, making it the correct choice.