Lesson in Slope

Slope-Intercept Word Problems

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Identifying Slope in a Word Problem

The slope in a word problem is the rate of change. As it is a rate, you will often see the slope associated with words like "each" or "per" (ex: she paid x dollars for each item, he charged x dollars per hour).

Identifying Y-Intercept in a Word Problem

The y-intercept in a word problem is the starting point or initial value.

Now you practice writing equations...

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Multiple Choice

Suppose that a bike rents for $4 plus $1.50 per hour. Write an equation in slope-intercept form that models this situation.

• y = 4x + 1.50

• y = 1.50x + 4

Multiple Choice

An electrician charges $90 per hour plus a $50 travelling fee. Which equation represents the total cost of a repair by an electrician after x hours?

• y = 50 - 90x

• y = 90x + 50

• y = -50x + 90

• y = -90 - 50x

Sometimes the order of the equation can be switched, like y = b + mx.

Remember that the slope (rate of change) will always be the coefficient of x.

Multiple Choice

A canoe rental service charges a $20 transportation fee and $30 dollars an hour to rent a canoe. Write an equation representing the cost, y, of renting a canoe for x hours.

• y = 20 + 30x

• y = 30 + 20x

• y = 50x

• y = 60x

Multiple Choice

Daniel is paid $10 per week for selling newspaper subscriptions. He is also paid $3.50 for each new customer, x, that signs up for the subscription. Which equation represents the amount, y, Daniel earns per week?

• y = 3.5x

• y = 10 + x

• y = 10 + 35x

• y = 10 + 3.5x

Also, don't get hung up on the variables "x" and "y". Those can be changed to other letters.

Multiple Choice

For babysitting, Nicole charges a flat fee of $3, plus $5 per hour. Write an equation for the cost, C, after h hours of babysitting.

• C = 5h + 3

• C = 3h + 5

• h = 5C + 3

• h = 3C + 5

Multiple Choice

Talk Time Phone Company charges $0.12 per minute of phone use plus a monthly service fee of $8.00 for its phone service. Which equation below can be used to find c, the total cost for one month when m, minutes are used?

• c = 0.12m + 8m

• m = 0.12c + 8

• c = 0.12m + 8

• c = 0.20m

Hint: Watch the order on this next one!

Multiple Choice

A plumber charges $25 for a service call plus $50 per hour of service. Write an equation in slope-intercept form for the cost, C, after h hours of service.

• C = 25 + 50h

• C = 50 + 25h

• h = 25 + 50C

• h = 50 + 25C

Read your problem and really think about what is happening. Your rate of change will not always be positive.

Multiple Choice

A family buys a case of water with 48 bottles and drinks 5 bottles per day. Which equation shows the number of bottles left after x days?

• y = 48x + 5

• y = -5 + 48x

• y = -5x - 48

• y = 48 - 5x