Reading Graphs — Practice Problems and Worked Solutions

The formulas you need here

16 worked problems

Every step is generated and checked by a computer algebra system.

1. 1.

   Find the output shown by the rule.

   $$y=2x+1,x=3$$

   Answer: $y=7$

   Step-by-step solution

   1. $$\text{Read inputs horizontally and outputs vertically.}$$
   2. $$m=\frac{\text{change in }y}{\text{change in }x}$$
   3. $$y=7$$
2. 2.

   Choose the rule that matches every plotted point.

   $$\{(0,1),(1,3),(2,5)\}$$

   Answer: $y=2x+1$

   Step-by-step solution

   1. $$\text{Read inputs horizontally and outputs vertically.}$$
   2. $$m=\frac{\text{change in }y}{\text{change in }x}$$
   3. $$y=2x+1$$
3. 3.

   Find the slope between the two points.

   $$(1,2)\text{ and }(3,6)$$

   Answer: $m=2$

   Step-by-step solution

   1. $$\text{Read inputs horizontally and outputs vertically.}$$
   2. $$m=\frac{\text{change in }y}{\text{change in }x}$$
   3. $$m=2$$
4. 4.

   Identify the y-intercept as a point.

   $$y=-3x+4$$

   Answer: $(0,4)$

   Step-by-step solution

   1. $$\text{Read inputs horizontally and outputs vertically.}$$
   2. $$m=\frac{\text{change in }y}{\text{change in }x}$$
   3. $$(0,4)$$
5. 5.

   Describe the graph from left to right.

   $$y=-2x+5$$

   Answer: $\text{decreasing}$

   Step-by-step solution

   1. $$\text{Read inputs horizontally and outputs vertically.}$$
   2. $$m=\frac{\text{change in }y}{\text{change in }x}$$
   3. $$\text{decreasing}$$
6. 6.

   Find the change in output.

   $$y=3x-1,x:2\to 5$$

   Answer: $\Delta y=9$

   Step-by-step solution

   1. $$\text{Read inputs horizontally and outputs vertically.}$$
   2. $$m=\frac{\text{change in }y}{\text{change in }x}$$
   3. $$\Delta y=9$$
7. 7.

   Find the output shown by the rule.

   $$y=3x+2,x=4$$

   Answer: $y=14$

   Step-by-step solution

   1. $$\text{Read inputs horizontally and outputs vertically.}$$
   2. $$m=\frac{\text{change in }y}{\text{change in }x}$$
   3. $$y=14$$
8. 8.

   Choose the rule that matches every plotted point.

   $$\{(0,2),(1,5),(2,8)\}$$

   Answer: $y=3x+2$

   Step-by-step solution

   1. $$\text{Read inputs horizontally and outputs vertically.}$$
   2. $$m=\frac{\text{change in }y}{\text{change in }x}$$
   3. $$y=3x+2$$
9. 9.

   Find the slope between the two points.

   $$(2,1)\text{ and }(5,7)$$

   Answer: $m=2$

   Step-by-step solution

   1. $$\text{Read inputs horizontally and outputs vertically.}$$
   2. $$m=\frac{\text{change in }y}{\text{change in }x}$$
   3. $$m=2$$
10. 10.

    Identify the y-intercept as a point.

    $$y=4x-7$$

    Answer: $(0,-7)$

    Step-by-step solution

    1. $$\text{Read inputs horizontally and outputs vertically.}$$
    2. $$m=\frac{\text{change in }y}{\text{change in }x}$$
    3. $$(0,-7)$$
11. 11.

    Describe the graph from left to right.

    $$y=5x-2$$

    Answer: $\text{increasing}$

    Step-by-step solution

    1. $$\text{Read inputs horizontally and outputs vertically.}$$
    2. $$m=\frac{\text{change in }y}{\text{change in }x}$$
    3. $$\text{increasing}$$
12. 12.

    Find the change in output.

    $$y=2x+6,x:1\to 4$$

    Answer: $\Delta y=6$

    Step-by-step solution

    1. $$\text{Read inputs horizontally and outputs vertically.}$$
    2. $$m=\frac{\text{change in }y}{\text{change in }x}$$
    3. $$\Delta y=6$$
13. 13.

    Find the output shown by the rule.

    $$y=-x+3,x=5$$

    Answer: $y=-2$

    Step-by-step solution

    1. $$\text{Read inputs horizontally and outputs vertically.}$$
    2. $$m=\frac{\text{change in }y}{\text{change in }x}$$
    3. $$y=-2$$
14. 14.

    Find the slope between the two points.

    $$(0,4)\text{ and }(2,0)$$

    Answer: $m=-2$

    Step-by-step solution

    1. $$\text{Read inputs horizontally and outputs vertically.}$$
    2. $$m=\frac{\text{change in }y}{\text{change in }x}$$
    3. $$m=-2$$
15. 15.

    Describe the graph from left to right.

    $$y=7$$

    Answer: $\text{constant}$

    Step-by-step solution

    1. $$\text{Read inputs horizontally and outputs vertically.}$$
    2. $$m=\frac{\text{change in }y}{\text{change in }x}$$
    3. $$\text{constant}$$
16. 16.

    Identify the y-intercept as a point.

    $$y=6x+1$$

    Answer: $(0,1)$

    Step-by-step solution

    1. $$\text{Read inputs horizontally and outputs vertically.}$$
    2. $$m=\frac{\text{change in }y}{\text{change in }x}$$
    3. $$(0,1)$$

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