Topic 2 - Linear Equations

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The equation y = −3x + 7 represents the amount of water y left in a 7-gallon tub after x minutes.

Where does the graph of the equation intersect the y-axis and the x-axis?

y-axis: (​ (a)   ,​ (b)   ) x-axis: (​ (c)   , ​ (d)   )

• 0
• 7
• 7/3
• -3

At 2 hours before sunset, the temperature is 0°F. At 2 hours after sunset, the temperature is −4°F . Identify the equation representing the temperature y , in °F, at x hours after sunset.

y = ​ (a)   x + ​ (b)  

• -1
• -2
• -4
• 2
• 1

Rachel hikes at a steady rate from a ranger station to a campground 20 mi away. After 2 h, she is 13 mi from the campground. After 4 h, she is 6 mi from the campground. A graph shows her distance y from the campground, in miles, after x hours. What is the slope of the graph, and what does it represent?

• 20; Rachel’s initial distance from the campground

• −3.5 ; the rate Rachel’s distance from the campground changes per hour

• 3.5; Rachel’s initial distance from the campground

• 20; Rachel’s final distance from the campground

Which line passes through the points (−4, –0.25) and (1.8, −3.15) ?

• y = 0.5x + 2.25

• y = −0.5x − 2.25

• y = −2x − 7.75

• y = 2x + 7.75

Which is the graph of the line y − 2 = 3(x − 1) ?

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Isobel is pulling water up from an old-fashioned well. She lifts the bucket of water at a rate of 4 ft/s, and after 1 s, the bucket is 1 ft below the top of the well. What is the equation, in point-slope form, of the line, where y represents the height, in feet, of the bucket relative to the top of the well after x seconds?

y + ​ (a)   =​ (b)   (x + ​ (c)   )

• 1
• 4
• -1
• 2
• -2

Select all the sets of ordered pairs that the graph of the equation y − 1 = −2(x − 2) contains.

• (0, −2) and (1, 3)

• (−1, 7) and (2, 1)

• (1, 2) and (4, 3)

• (0, 5) and (−2, 9)

• (3, −1) and (2, −1)

Which equation represents the graphed line?

• y − 1 = −2(x − 3)

• y − 1 = −2(x + 3)

• y + 1 = −2(x − 3)

• y + 1 = −2(x + 3)

The table shows the number of condo sales per month for a new condo building. Select all the equations that could represent the number of sales.

• y − 11 = −3(x − 0)

• y + 1 = −3(x − 2)

• y + 11 = 3(x − 0)

• y −1 = −3(x + 8)

• y − 2 = −3(x − 3)