Slope and Angle Relationships

The video tutorial explains how to determine the angle a line makes with the horizontal by using the slope. It introduces the concept of slope as the tangent of the angle and demonstrates how to calculate the angle using the tangent inverse. An example problem is provided to find the slope from a linear equation, and the process of graphing the line is shown. The tutorial also covers how to adjust a negative angle to a positive one by adding 180 degrees.

What is the relationship between the slope of a line and the tangent of the angle it makes with the horizontal?

• The slope is the cosine of the angle.

• The slope is the cotangent of the angle.

• The slope is the sine of the angle.

• The slope is the tangent of the angle.

In the tangent ratio, what does the 'opposite' side represent in the context of a line's slope?

• The change in X

• The base of the triangle

• The change in Y

• The hypotenuse

What does the 'adjacent' side represent in the tangent ratio for a line's slope?

• The base of the triangle

• The hypotenuse

• The change in Y

• The change in X

How do you find the angle of a line if you know its slope?

• Use the cosine inverse of the slope.

• Use the tangent inverse of the slope.

• Use the sine inverse of the slope.

• Use the cotangent inverse of the slope.

What is the first step in finding the slope from the equation 3x + 2y = 6?

• Subtract 3x from both sides.

• Add 6 to both sides.

• Rearrange the equation to slope-intercept form.

• Multiply both sides by 2.

What is the slope of the line given by the equation y = -3/2x + 3?

• 3/2

• -3/2

• -2/3

• 2/3

What is the formula for converting a line equation to slope-intercept form?

• y = bx + m

• x = my + b

• x = by + m

• y = mx + b

What is the angle in degrees when the tangent inverse of the slope -3/2 is calculated?

• 33.7 degrees

• -33.7 degrees

• 56.3 degrees

• -56.3 degrees

What is the y-intercept of the line y = -3/2x + 3?

• 3

• -3

• 0

• 6

What is the graphical representation of a line with a negative slope?

• A line that rises from left to right

• A line that falls from left to right

• A vertical line

• A horizontal line