Writing Linear Equations from Word Problems

The video tutorial covers how to write linear equations from word problems, using examples like calculating profit from selling t-shirts and caps. It explains the slope-intercept and standard forms of linear equations and demonstrates converting between these forms. The video concludes with a real-world example of modeling a plumber's charges using a linear equation.

What is the profit equation if the profit P depends on the number of shirts sold s and the number of caps sold c?

• P = 10s + 5c

• P = 10s - 5c

• P = 5s + 10c

• P = 5s - 10c

If 30 shirts and 30 caps are sold, what is the total profit?

• $450

• $600

• $650

• $700

How much profit is made from selling 15 shirts and 10 caps?

• $150

• $175

• $200

• $225

What is the profit if 12 shirts and 20 caps are sold?

• $280

• $260

• $240

• $220

Which form of linear equation is expressed as y = mx + b?

• Exponential form

• Quadratic form

• Slope-intercept form

• Standard form

What is the standard form of a linear equation?

• y = mx + b

• ax + by = c

• y = a^x

• y = ax^2 + bx + c

How do you convert the equation 600 = 5s + 10c to slope-intercept form?

• y = -2x + 60

• y = 1/2x + 60

• y = 2x + 60

• y = -1/2x + 60

If a plumber charges $50 for a house call and $25 per hour of work, what is the equation to model this scenario?

• C = 50h + 25

• C = 25h + 50

• C = 25 + 50h

• C = 50 + 25h

Using the plumber's equation, how much would it cost if the plumber worked for 2 hours?

• $125

• $100

• $75

• $150

What is the slope in the equation y = -1/2x + 60?

• 1/2

• -1/2

• 60

• -60