Exploring Algebraic Manipulation of Linear Functions

The video tutorial covers algebraic manipulation of linear functions, including finding equations in point-slope, slope-intercept, and standard forms. It explains graphing techniques for linear equations and applies these concepts to solve real-world problems, such as calculating costs and analyzing race data. The tutorial emphasizes understanding graph features like intercepts and slopes.

What is the point-slope form of a line passing through the points (7, 4) and (3, -4)?

• y + 4 = -2(x + 7)

• y - 4 = -2(x - 7)

• y + 4 = 2(x + 7)

• y - 4 = 2(x - 7)

What is the slope-intercept form of the line with the equation y - 4 = 2(x - 7)?

• y = -2x - 10

• y = 2x + 10

• y = 2x - 10

• y = -2x + 10

What is the standard form of the line with the equation y = 2x - 10?

• -2x + y = -10

• 2x - y = 10

• -2x - y = 10

• 2x + y = -10

To graph the equation y = 2/3x - 2, where do you start?

• At the origin

• At the y-intercept of 2

• At the y-intercept of -2

• At the x-intercept of 2

For the equation y = -3x + 1, what is the slope?

• -3

• 3

• -1/3

• 1/3

How do you find the x-intercept of the equation 2x - 5y = 10?

• Set x to 0 and solve for y

• Set y to 0 and solve for x

• Set y to 1 and solve for x

• Set both x and y to 0

What is the y-intercept of the equation -4x + 3y = -24?

• 8

• -8

• 6

• -6

What is the hourly fee charged by the recording studio?

• $150

• $450

• $75

• $300

What is the base fee for renting the recording studio?

• $450

• $150

• $300

• $75

How long did it take Jaden to finish the race?

• 60 minutes

• 100 minutes

• 80 minutes

• 10 minutes