Lines Practice Problems

Here you will find lines practice problems which is also known as linear functions. Your understanding of lines will be helpful when studying Caluclus. Visit this page directly at hunkim.com/lines

1. In what quadrants is the line $y=3x+2$ found?
   Solution
   I, II, III
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2. Find the slope of $y=5-3x$
   Solution
   $-3$
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3. Find the y-intercept of $y=2x+5$
   Solution
   $5$
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4. Find the x-intercept of $3x-4y=1$
   Solution
   $\frac{1}{3}$
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5. Find the y-intercept of $\frac{2x}{3}-\frac{3y}{5}=\frac{1}{2}$
   Solution
   $-\frac{5}{6}$
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6. What slope is perpendicular to $m=-\frac{3}{4}$?
   Solution
   $\frac{4}{3}$
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7. What is the slope of the line $x=0$?
   Solution
   Undefined
   Video will be uploaded soon…
   Slope is undefined (vertical line)
8. What is the slope of the line $y=-1$?
   Solution
   $0$
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9. What is the slope of the line $y=x$?
   Solution
   $1$
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10. Given $y=2x+5$, is the point $(3,11)$ on this line?
    Solution
    Yes
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11. Given $3y-x=2$, is the point $(2,3)$ on this line?
    Solution
    No
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12. Find the slope given the points $A(2,-2)$ and $B(5,-17)$
    Solution
    $-5$
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13. Given $3y=2-5x$, when $y=2$, solve $x$
    Solution
    $-\frac{4}{5}$
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14. Find the slope in the diagram below:
    
    Solution
    $-2$
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15. See diagram below. When $x=10$, what is the value of $y$?
    
    Solution
    $34$
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16. A line contains the points $(2,5)$ and $(6,17)$
    True or False: These points are found on the line $y-2=3(x-1)$
    Solution
    True
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17. A line contains the points $(2,5)$ and $(6,17)$
    The equation of the line is $y=mx+b$. Find $b$
    Solution
    $-1$
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18. $3-\frac{2}{3}x=6y$ can be written in the general equation form
    $Ax+By+C=0, A>0$ and $A, B, C\in \mathbb{Z}$. Find $A$
    Solution
    $2$
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19. $6, 9, 12, ...$ Find the value of the 1000th number
    Solution
    $3003$
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20. Does the following table represent points on a line?
    
    Solution
    Yes
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21. Find the missing value in the table below:
    
    Solution
    $3.8$
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22. How long is this line segment?
    
    Solution
    $5$
    
    
23. True or False: $y=\frac{-2}{3}x+\frac{1}{5}$ is the same line as $y=\frac{2}{-3}x+0.2$
    Solution
    True
    
    
24. $4y-\frac{2}{3}x=5$. Write the equation in standard form: $Ax+By=C$. $A, B, C\in\mathbb{Z}$ and $A>0$
    Solution
    $2x-12y=-15$
    
    
25. Line $L_1$ is parallel to $L_2$. $L_1=3x-2$. Find $L_2$ in the form $y=mx+b$ if it goes through the point $(1,5)$
    Solution
    $y=3x+2$
    
    
26. Line $L_1$ is perpendicular to $L_2$. If $L_1=\frac{2}{3}x+1$ find the equation of $L_2$ in the form $y=mx+b$ if it has an x-intercept of $3$
    Solution
    $y=\frac{-3}{2}x+\frac{9}{2}$
    
    
27. Point: $A(2,7)$ and $B(a,3a)$. Given the slope is 2, find $a$.
    Solution
    $3$
    
    
28. Equation of the Line A below in the form $y=mx+b$?
    
    Solution
    $y=-2x+4$
    
    
29. Equation of Line B below in the form $y=mx+b$?
    
    Solution
    $y=\frac{1}{2}x+3$
    
    
30. Draw a line through the points in the gas-time graph below:
    
    1. Extrapolate the time when you run out of gas?
       Solution
       $t=22$
    2. If you gas tank is full at $t=0$, what percent of your tank is full at $t=5$?
       Solution
       $\approx77.3$
    3. What is the meaning of the slope of this graph?
       Solution
       Fuel efficiency (the rate of change of gas with respect to time)
       
       
31. Consider the pattern 5, 8, 11, 14, …
    1. The variable $f$ represents the figure number. Figure 1 contains the number 5 and figure 2 contains the number 8 and so on. Find the equation $n=af+b$, where $n$ represents the number at a particular figure number.
       Solution
       $f=3f+2$
       
       
    2. Find the 100th number.
       Solution
       $302$
       
       
32. See figures 1 to 4 below. Figure 1 has 2 squares and figure 4 has 11 squares. How many squares are in figure 43?
    
    Solution
    $128$
    
    
33. Does the following table of values represent points on a line?
    
    Solution
    No
    
    
34. Money is a function of time in hours: $M(t)=20t+50$.
    1. How much do you get paid for working 0 hours?
       Solution
       $\$50$
       
       
    2. How much do you get paid if you work for 8 hours?
       Solution
       $\$210$
       
       
    3. How many hours do you have to work to earn $280? Assume there is no overtime pay.
       Solution
       $11.5$ hours
       
       
35. A line has a y-intercept of 2 and goes through the point $(6,4)$. Find the equation of this line in slope-intercept form.
    Solution
    $y-2=\frac{1}{3}(x-0)$ or $y-4=\frac{1}{3}(x-6)$
    
    
36. $f(x)=\pi x+0.2$. $g(x)$ goes through the origin and never intersects with $f(x)$. What is the equation of $g(x)$?
    Solution
    $g(x)=\pi x$
    
    
37. $f(x)=3x-2$. $g(x)=3x+5$. How many units up should we shift $f(x)$ up in order to make the lines coincidental (infinite solutions).
    Solution
    $7$
    
    
38. The following table of values represents a line. Find the missing value below:
    
    Solution
    $24$
    
    
39. How many solutions? Solve the system of equations:
    $x+y=2$ and $2y=4-2x$
    Solution
    $\infty$
    
    
40. $f(x)=2x$ and $g(x)=2+x-1+x$
    Solve $f(x)=g(x)$
    Solution
    No solution
    
    
41. Is $(1,5)$ a point of intersection for the system:
    $x+2y=13$ and $3x-y=-3$?
    Solution
    No
    
    
42. Is $(1,6)$ a point of intersection for the system:
    $x+2y=13$ and $3x-y=-3$?
    Solution
    Yes
    
    
43. $x+y=2$ and $y=3$
    1. Solve by graphing
       
    2. Use substitution to find the coordinates of the point of intersection
       Solution
       $(-1,3)$
       
       
44. $2x+3y=12$ and $2y=8+4x$
    1. Solve by using graphing
       Solution
       
    2. Use substitution to find the coordinates of the point of intersection
       Solution
       $(0,4)$
       
       
    3. Use elimination to find the coordinates of the point of intersection
       Solution
       $(0,4)$
       
       
45. Systems of equations word problems:
    1. You have 4 more cookies than your friend.  You and your friend have 18 cookies combined.  How many cookies do you have?
       Solution
       $11$
       
       
    2. You have a total of 20 bills which consist of $10 and $5 bills.  How many $10 bills do you have if the total value of your money is $140?
       Solution
       $8$
       
       
    3. 3 nuts and 2 bolts weigh 12 kg and 2 nuts minus 3 bolts weigh 5 kg. How heavy is one bolt in grams?
       Solution
       $692$
       
       
46. Challenge:
    1. Line $L_2$ is the inverse of $L_1$. Given $L_1$ has a slope of $\frac{3}{2}$, find the slope of $L_2$.
       Solution
       $\frac{2}{3}$
       
       
    2. The cost to insure jewellery is a fixed amount plus a percentage of the value of the jewellery.  It costs $32 to insure $1000 worth of jewellery or $44.50 to insure $3500 worth of jewellery.  What is the fixed amount to insure jewellery?
       Solution
       $27$
       
       
    3. An airplane travels 1600 km in 4 hours with the wind.  The same trip takes 5 hours against the wind.  What is the speed of the plane in still air?
       Solution
       $360$
       
       
    4. How many ounces of 20% hydrochloric acid solution and 70% hydrochloric acid solution must be mixed to obtain 20 ounces of 50% hydrochloric acid solution?
       Solution
       8 oz. weak acid and 12 oz. strong acid
       
       
    5. $f(x)=2-\frac{x}{2}$. What is the minimum distance between this point and the point $(5,2)$?
       Solution
       $\sqrt{5}$