Solving Linear Equations and Functions

The video tutorial covers solving linear equations using the distributive property, additive and multiplicative inverses, and graphing techniques. It includes practice problems and a real-world application involving a walk-a-thon scenario to illustrate the concepts.

What is the first step in solving an equation with parentheses using the distributive property?

• Subtract the constant term

• Multiply each term inside the parentheses by the factor outside

• Add the coefficients together

• Divide the equation by the coefficient

When solving the equation 3y - 4 = 6 - 2y, what is the coefficient of y after using the additive inverse?

• 4

• 6

• 5

• 3

In the equation 12n + 6 = 54 - 9n, what is the value of n after solving?

• 6

• 5

• 4

• 3

What mistake did Clara make when she got different values on both sides of her equation?

• She added instead of subtracted

• She distributed subtraction incorrectly

• She multiplied by the wrong factor

• She forgot to use the additive inverse

How can you verify the solution of a linear equation?

• By dividing the solution by the coefficient

• By adding the solution to both sides

• By multiplying the solution by any number

• By checking if the solution satisfies the original equation

What is the correct equation for a line with a slope of 1/4 and a y-intercept of 5/4?

• y = 1/4x + 5/4

• y = 5/4x + 1/4

• y = 1/4x - 5/4

• y = 5/4x - 1/4

In the walk-a-thon example, what does the slope of -3 represent?

• The number of miles walked per hour

• The number of hours remaining per mile

• The number of hours walked per mile

• The number of miles remaining per hour

What is the y-intercept in the equation y = -3x + 21 for the walk-a-thon example?

• 3

• -3

• 0

• 21

If you start walking at 4 hours with 9 miles remaining, what is the total distance walked after 6 hours?

• 6 miles

• 21 miles

• 12 miles

• 18 miles

How does the equation y = -3x + 21 change if you start at 5.5 hours with 4.5 miles remaining?

• The slope becomes -4

• The y-intercept changes to 4.5

• The equation remains the same

• The slope becomes -3.5