Writing Linear Equations from Word Problems

The video tutorial discusses writing equations for a fundraising problem involving selling t-shirts and caps. It introduces variables for unknowns, formulates a profit equation, and provides examples of calculating profit. The video also explains different forms of linear equations, focusing on converting standard form to slope-intercept form for graphing purposes.

What are the three unknown variables in the problem of eighth graders selling t-shirts and caps?

• Number of t-shirts, number of caps, and total cost

• Number of t-shirts, number of caps, and revenue

• Number of t-shirts, number of caps, and profit

• Number of t-shirts, number of caps, and total sales

What is the profit equation derived from the number of t-shirts and caps sold?

• P = 10s + 5c

• P = 10s - 5c

• P = 5s - 10c

• P = 5s + 10c

If the students sell 30 t-shirts and 50 caps, what is their total profit?

• $500

• $700

• $650

• $600

How much profit do the students make if they sell 15 t-shirts and 10 caps?

• $150

• $125

• $100

• $175

What is the profit when 12 t-shirts and 20 caps are sold?

• $240

• $200

• $260

• $220

Which form of linear equation is most natural when the values of one variable depend on another?

• 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 = ax + b

• ax + by = 0

What is the first step in converting a standard form equation to slope-intercept form?

• Divide every term by the coefficient of y

• Subtract the x term from both sides

• Multiply every term by the coefficient of y

• Add the x term to both sides

What is the slope-intercept form of the equation 600 = 5s + 10c?

• y = -2x + 60

• y = 2x + 60

• y = 1/2x + 60

• y = -1/2x + 60

Why is it helpful to convert an equation to slope-intercept form?

• It makes the equation easier to differentiate

• It simplifies the equation for integration

• It allows the equation to be graphed on a calculator

• It makes the equation easier to solve manually