Understanding Tangent Lines and Slopes

What does it mean for two lines to be parallel?

• They have different slopes.

• They are perpendicular.

• They have the same slope.

• They intersect at one point.

How do you find the slope of a line from its equation?

• By finding the x-intercept.

• By converting it to slope-intercept form.

• By converting it to point-slope form.

• By finding the y-intercept.

What is the slope of the line given by the equation -2y = -8x - 13?

• 2

• -2

• 4

• -4

Which rule is used to find the derivative of a function that is a quotient of two expressions?

• Product rule

• Quotient rule

• Power rule

• Chain rule

What is the simplified form of the derivative of the function x - 2 over x + 2?

• 2 over (x + 2)

• 2 over (x + 2)^2

• 4 over (x + 2)^2

• 4 over (x + 2)

What equation do you solve to find the x-values where the tangent lines are parallel to the given line?

• x^2 + 4 = 0

• (x + 2)^2 = 1

• x + 2 = 0

• x + 2 = ±1

What are the x-values where the tangent lines are parallel to the given line?

• 2 and -2

• 0 and -2

• -1 and -3

• 1 and 3

How do you find the y-coordinate for a point of tangency?

• By using the slope-intercept form.

• By substituting the x-value into the original function.

• By solving the equation of the line.

• By using the derivative.

What is the ordered pair for the point of tangency when x = -1?

• (-1, 3)

• (-1, -3)

• (-1, 5)

• (-1, -5)

What is the equation of the tangent line at the point (-3, 5)?

• y - 5 = 4(x + 3)

• y - 5 = 4(x - 3)

• y + 5 = 4(x + 3)

• y + 5 = 4(x - 3)