Slope, Inequalities, and Functions

The video tutorial covers solving various math problems, including graph analysis, coin calculations, absolute value equations, inequalities, and determining line equations from graphs. Each problem is broken down step-by-step, highlighting key concepts such as slope, y-intercept, substitution, and handling inequalities. The tutorial emphasizes understanding the process and reasoning behind each solution.

Which choice correctly represents the graph of two lines with y-intercepts of 3 and slopes of 1 and -1?

• Choice A

• Choice C

• Choice B

• Choice D

If Yoshi has twice as many dimes as nickels and a total of $1, how many nickels does she have?

• 2

• 3

• 5

• 4

What is the value of n if 10d + 5n = 100 and d = 2n?

• 6

• 5

• 4

• 3

What are the possible values of x if 10|x| = 2.5?

• 1 and -1

• 0.25 and -0.25

• 2 and -2

• 0.5 and -0.5

What is the result of dividing 2.5 by 10?

• 0.025

• 0.25

• 2.5

• 25

When solving the inequality 1 - 2x > 3(x - 2), what is the first step?

• Divide by -2

• Add 2x to both sides

• Distribute the 3

• Subtract 1 from both sides

What happens to the inequality sign when you divide both sides by a negative number?

• It becomes an equality

• It reverses

• It stays the same

• It disappears

What is the slope of the line if the change in y is -1 and the change in x is 2?

• -2

• -1/2

• 1/2

• 2

If a line has a slope of -1/2 and a y-intercept of 1.5, what is its equation?

• y = -1/2x + 1.5

• y = 1/2x - 1.5

• y = 2x - 3

• y = -2x + 3

What is the simplified form of the equation 2y = -x + 3?

• -x - 2y = 3

• -x + 2y = 3

• x - 2y = 3

• x + 2y = 3