Test 3. Linear function

 1. What is the equation of the line that passes through the points (0, 2) and (4, 7)?

Express your answer in y = mx + b form.

 а)  y = 2;     

 b)  y = ¹/₂ x + 5;     

 c)  y = 4x + 2;     

 d)  y = ⁵/₄ x + 2.

 2. Find the equation of the line with slope m = 2 that passes through the point (⁵/₄, 3).

Express your answer in y = mx + b form.

 а)  y = ¹/₂ x + 2;     

 b)  y = 3x + ⁵/₄;     

 c)  y = 2x + ¹/₂;     

 d)  y = ⁵/₄ x + 3.

 3. Suppose Bob has 4 candies. He then earns candies at a rate of 14 candies per week. Which of the following formulas is the most reasonable rate to know how many candies Bob has on any given day?

 а)  C = 2d + 4;     

 b)  C = ²/₇ d + 4;     

 c)  C = ¹/₇ d + 4;     

 d)  C = 7d + 4.

 4. After one hour of working, Billy has three dollars. At the end of eight hours, Billy has fifty dollars. Choose the most correct linear function representing this scenario if t represents time, and d represents dollars.

 а)  d = ⁴⁷/₇ t – ²⁶/₇;     

 b)  t = ⁴⁷/₇ d + ²⁶/₇;     

 c)  t = ⁴⁷/₇ d – ²⁶/₇;     

 d)  d = ⁴⁷/₇ t + ²⁶/₇.

 5. Determine the equation of a line that passes through the points (6, 6) and (0, 5).

 а)  y = ¹/₆ x + 6;     

 b)  y = ¹/₆ x + 5;     

 c)  y = ¹/₆ x + ¹/₆;     

 d)  y = ¹/₆ x – 5.

 6. What equation is perpendicular to

y = 5x + 2

and passes through (6, 10)?

 а)  y = –¹/₅ x – 16;     

 b)  y = –¹/₅ x + ⁵⁶/₅;     

 c)  y = –5 x + 12;     

 d)  y = –¹/₅ x + 11.

 7. What equation is perpendicular to

y = –¹/₅ x + 3

and passes through (2, 4)?

 а)  y = ²/₅ x – ⁴/₃;     

 b)  y = ⁵/₂ x – ³/₂;     

 c)  y = –5x – ¹/₂;     

 d)  y = ⁵/₂ x – 1.

 8. What equation is perpendicular to

y = ³/₇ x + 12

and passes through (5, 4)?

 а)  y = –⁷/₃ x + ⁴⁷/₃;      

 b)  y = –⁷/₃ x – ¹⁶/₃;     

 c)  y = –⁷/₃ x – ⁴⁷/₄;      

 d)  y = –⁷/₃ x – 16.

 9. A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly. He started at 90 kilograms and gained weight at a constant rate. After 8 months, he weighed 138 kilograms.

Let W(t) denote the sumo wrestler’s weight W (measured in kilograms) as a function of time t (measured in months).

Write the function’s formula. 

W(t) = ?  

 а)  90 + 8t;     

 b)  90 t + 8;     

 c)  90 + 6t;     

 d)  90t + 6.

10. What is the slope of the line through (–5, –10) and (–1, 5)?

 а)  –⁴/₁₅;      b)  ¹⁵/₄;     

 c)  –¹⁵/₄;      d)  ⁴/₁₅.

11. What is

y + 4 = –6(x + 6)

written in standard form?

 а)  y = –6x – 40;     

 b)  6x + y = 2;     

 c)  y = –6x + 2;     

 d)  6x + y = – 40.

12. What is the y-intercept of

y = –3x – 2?

 а)  (–2, 0);      b)  (0, –2);     

 c)  (–3, 0);      d)  (0, –3).