Real-World Slope Intercept Form: Conversion & Applications

Convert the equation 2x - 4y = 8 into slope-intercept form. What does the y-intercept tell you about the situation it represents?

• The slope-intercept form is y = 2x + 4. The y-intercept of 4 indicates a maximum value.

• The slope-intercept form is y = (3/2)x + 2. The y-intercept of 2 suggests a positive initial condition.

• The slope-intercept form is y = -2x + 8. The y-intercept of 8 shows a negative starting point.

• The slope-intercept form is y = (1/2)x - 2. The y-intercept of -2 indicates that when x = 0, the value of y is -2, which may represent a starting point or initial condition in the context of the situation.

A car rental company charges a flat fee of $20 plus $0.50 per mile driven. Write the equation in slope-intercept form to represent the total cost (C) as a function of miles driven (m).

• C = 0.50m + 20

• C = 0.50m - 20

• C = 20m + 0.50

• C = 0.20m + 20

The equation of a line is given as y - 5 = 2(x - 3). Convert this to slope-intercept form and explain what the slope indicates about the relationship between x and y.

• y = -2x + 3

• y = 2x + 5

• y = 2x - 1

• y = 3x - 1

A school is planning to build a new gym. The cost of construction is estimated to be $50,000 plus $10,000 for each additional square foot. Write the equation in slope-intercept form and interpret the slope.

• C = 5000x + 30000

• C = 20000x + 40000

• C = 15000x + 60000

• C = 10000x + 50000

Convert the equation 5x + 2y = 10 into slope-intercept form. What does the slope represent in a real-world scenario?

• The slope indicates the total value of y when x is zero.

• The slope shows the maximum value of y for any given x.

• The slope represents the rate of change of y with respect to x, indicating how much y decreases for each unit increase in x in a real-world scenario.

• The slope represents the initial value of y before any changes in x.

The line representing the temperature in a city over time is given by the equation y = -2x + 30. What does the slope tell you about the temperature change?

• The slope of -2 suggests the temperature fluctuates randomly without a trend.

• The slope of -2 indicates the temperature decreases by 2 degrees for each unit of time.

• The slope of -2 indicates the temperature increases by 2 degrees for each unit of time.

• The slope of -2 means the temperature remains constant over time.

A local gym has a membership fee of $25 and charges $10 per class attended. Write the equation in slope-intercept form and calculate the total cost for attending 8 classes.

• $85

• $115

• $95

• The total cost for attending 8 classes is $105.

Convert the equation 3x - y = 12 into slope-intercept form. What does the y-intercept represent in the context of a budget for a project?

• The y-intercept indicates the total expenses for the project.

• The y-intercept represents the profit expected from the project.

• The y-intercept shows the maximum budget limit for the project.

• The y-intercept represents the initial budget available for the project before any expenses are incurred.