Linear Equations and Their Properties

The video tutorial covers practice problems for lesson eight, focusing on translating equations to the form y=mx+b. It includes five problems: identifying parallel graphs with the same y-intercept, comparing two equations, finding a linear equation for a cable company's charges, matching graphs to situations based on slope and y-intercept, and calculating elevation changes on a mountain road. Each problem is explained with detailed steps and examples to enhance understanding.

Which of the following equations represents a line with a y-intercept of -8?

• y = 1/3x + 8

• y = 5x - 9

• y = 2x + 8

• y = 3x - 8

If two lines have the same slope but different y-intercepts, what can be said about their graphs?

• They are parallel.

• They are perpendicular.

• They coincide.

• They intersect at the origin.

In the equation y = 70x, what does the number 70 represent?

• The x-intercept

• The constant term

• The y-intercept

• The slope

What is the initial cost for a new customer if the service fee is $100 and the monthly charge is $70?

• $0

• $170

• $100

• $70

Which graph would represent a situation with a slope of 1/4 and a y-intercept of 8?

• A line passing through (0, 3) with a slope of 1/4

• A line passing through (0, 8) with a slope of 3

• A line passing through (0, 0) with a slope of 1/4

• A line passing through (0, 8) with a slope of 1/4

If a line has a slope of 3, what does this indicate about the line's steepness?

• It is steeper than a line with a slope of 1/4.

• It is horizontal.

• It is less steep than a line with a slope of 1/4.

• It is vertical.

What is the slope of a line that represents the perimeter of an equilateral triangle?

• 1

• 2

• 3

• 4

In the mountain road problem, what is the elevation at the starting point?

• 700 feet

• 4800 feet

• 6200 feet

• 5500 feet

How much does the elevation increase per mile on the mountain road?

• 6200 feet

• 5500 feet

• 700 feet

• 350 feet

What is the equation of the line representing the mountain road's elevation change?

• y = 350x + 4800

• y = 700x + 5500

• y = 350x + 5500

• y = 700x + 4800