Linear Equalities

Writing Equations and Inequalities From Verbal Descriptions

Multiple Choice

For babysitting, Nicole charges a flat fee of $5, plus $10 per hour. Which equation represents this scenario for the cost, y, after x hours of babysitting?

• 
  

  $$y=\ -5+10x$$

• $$y=5x-10$$

• $$y=\ 5x+10$$

• $$y=\ 5+10x$$

Multiple Choice

A business purchases a computer for $1500. The computer goes down in value $200 each year when the new model is released. Which of the following equations represents this scenario?

• 
  

  $$y=\ -1500x+200$$

• $$y=-200x+1500$$

• $$y=\ 1500x-200$$

• $$y=\ 1500+200x$$

Multiple Choice

You are running a concession stand at the basketball game. You sell hot dogs for $3 each and sodas for $1.50 each. At the end of night, you made $200. Let x represent the number of hot dogs sold and y represent the number of sodas sold.

Which equation that can be used to determine how many hot dogs and how many sodas were sold?

• $$y=200-1.5x$$

• $$y=200-3x$$

• $$1.50x+3y=200$$

• $$3x+1.50y=200$$

Multiple Choice

Your school is sponsoring a pancake dinner to raise money for a field trip. You estimate that 200 adults and 250 children will attend. Let x represent the cost of an adult ticket and y represent the cost of a child ticket. Which equation can be used to find what ticket prices to set in order to raise $3800?

• $$200x+250y=3800$$

• $$250x+200y=3800$$

• $$y=3800x-250$$

• $$y=3800-250x$$

Multiple Choice

The school rented buses and vans to go to a football. There were 8 vans and 12 buses for a total of  360 students. Let x represent the number of students in each van and y represent the number of students on each bus. Which equation represents this scenario?

• $$y=\ 360-8x-12y$$

• $$8x+12y=360$$

• $$12x+8y=360$$

• $$y=360-8x$$

Multiple Choice

Maya is investing in the stock market and has a maximum budget of $1,300 with which to purchase stock in two promising companies. Stock in the software company currently sells for $10 per share. Stock in the robotics company is currently trading at $12 per share.

Let x represent the number of shares in the software company and y represent the number of shares in the robotics company.

Which inequality in standard form describes this situation?

• $$12x+10y\le1300$$

• $$10x+12y\ge1300$$

• $$12x+10y\ge1300$$

• $$10x+12y\le1300$$

Multiple Choice

Brian is ordering a flower arrangement with roses and carnations. He doesn't want to spend more than $28 on the arrangement. Roses cost $5 each and carnations cost $2 each. . 

Let x represent the number of roses and y represent the number of carnations. 

Which inequality in standard form describes this situation?

• $$5x+2y\le28$$

• $$5x+2y\ge28$$

• $$5x+2y<28$$

• $$5x+2y>28$$

Multiple Choice

Burlington is hosting a city-wide arts festival at which vendors can pay to have a small booth or a large booth. The fee for a small booth is $40, whereas the fee for a large booth is $79. The city hopes to receive at least $2,100 in fees. 

Let x represent the number of small booths and y represent the number of large booths.

Which inequality in standard form describes this situation?

• $$40x+79y>2100$$

• $$79x+40y>2100$$

• $$79x+40y\ge2100$$

• $$40x+79y\ge2100$$

Multiple Choice

Which of the following is slope intercept form?

• $$y-y_1=m\left(x-x_1\right)$$

• $$y=mx+b$$

• $$Ax+By=C$$

• $$m=\frac{y_2-y_1}{x_2-x_1}$$

Multiple Choice

Which of the following is point slope form?

• $$y-y_1=m\left(x-x_1\right)$$

• $$y=mx+b$$

• $$Ax+By=C$$

• $$m=\frac{y_2-y_1}{x_2-x_1}$$

Multiple Choice

Which of the following is standard form?

• $$y-y_1=m\left(x-x_1\right)$$

• $$y=mx+b$$

• $$Ax+By=C$$

• $$m=\frac{y_2-y_1}{x_2-x_1}$$

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