2022 Linear Graphs Revision PDF

**Linear Graphs Revision** **Question 1**\ Define the terms gradient and [*y*]{.math.inline}-intercept. **Question 2**\ For each of the tables below, state the gradient. -----------------------------------------------------------------------------------------------------------------------------...

**Linear Graphs Revision** **Question 1**\ Define the terms gradient and [*y*]{.math.inline}-intercept. **Question 2**\ For each of the tables below, state the gradient. --------------------------------------------------------------------------------------------------------------------------------------------------- \ \ \ \ \ \ [*x*]{.math.display}\ [ − 2]{.math.display}\ [ − 1]{.math.display}\ {.math.display}\ {.math.display}\ {.math.display}\ ------------------------ ------------------------- ------------------------- ---------------------- ----------------------- ----------------------- \ \ \ \ \ \ [*y*]{.math.display}\ {.math.display}\ {.math.display}\ {.math.display}\ {.math.display}\ {.math.display}\ --------------------------------------------------------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------------------------------------------------------------------ \ \ \ \ \ \ [*x*]{.math.display}\ [ − 2]{.math.display}\ [ − 1]{.math.display}\ {.math.display}\ {.math.display}\ {.math.display}\ ------------------------ ------------------------- ------------------------- ------------------------- -------------------------- -------------------------- \ \ \ \ \ \ [*y*]{.math.display}\ {.math.display}\ [ − 4]{.math.display}\ [ − 8]{.math.display}\ [ − 12]{.math.display}\ [ − 16]{.math.display}\ ------------------------------------------------------------------------------------------------------------------------------------------------------------ **Question 3**\ For each of the tables below, state the [*y*]{.math.inline}-intercept. ------------------------------------------------------------------------------------------------------------------------------------------------- \ \ \ \ \ \ [*x*]{.math.display}\ [ − 2]{.math.display}\ [ − 1]{.math.display}\ {.math.display}\ {.math.display}\ {.math.display}\ ------------------------ ------------------------- ------------------------- ---------------------- ---------------------- ---------------------- \ \ \ \ \ \ [*y*]{.math.display}\ {.math.display}\ {.math.display}\ {.math.display}\ {.math.display}\ {.math.display}\ ------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------- \ \ \ \ \ \ [*x*]{.math.display}\ [ − 2]{.math.display}\ [ − 1]{.math.display}\ {.math.display}\ {.math.display}\ {.math.display}\ ------------------------ -------------------------- -------------------------- -------------------------- -------------------------- -------------------------- \ \ \ \ \ \ [*y*]{.math.display}\ [ − 25]{.math.display}\ [ − 30]{.math.display}\ [ − 35]{.math.display}\ [ − 40]{.math.display}\ [ − 45]{.math.display}\ --------------------------------------------------------------------------------------------------------------------------------------------------------------- **Question 4**\ Solve the following equations for [*x*]{.math.inline}. a. [2*x* + 6 = 0]{.math.inline} b. [3 − *x* =  − 9]{.math.inline} c. [12 + 3*x* =  − 6]{.math.inline} **Question 5**\ For each of the following linear graphs: i. Find the gradient, [*m*]{.math.inline}. ii. Find the [*y*]{.math.inline}-intercept, [*c*]{.math.inline}. iii. Using [*m*]{.math.inline} and [*c*]{.math.inline}, work out the rule: +-----------------+-----------------+-----------------+-----------------+ | c. |  | | | +=================+=================+=================+=================+ | a. |  | | | +-----------------+-----------------+-----------------+-----------------+ **Question 6**\ Find the [*x*]{.math.inline} and [*y*]{.math.inline} intercepts for the rules below. a. [*y* = 2*x* + 5]{.math.inline} b. [4*x* − 2*y* = 12]{.math.inline} **Question 7**\ Label the graphs below as having either a positive, negative, zero or undefined gradient.  ----------------------- --  **Question 8**\ Rudolph's Taxi Service charges \$2.50 for the first kilometre and \$1.10 for each additional kilometre. If the fare was \$47.60, how far did the taxi go? **Question 9**\ Gustav's fridge is not working.\ He called a repair company, and they are sending someone to repair the fridge. Company charges are: \$55 to come to your home, plus \$45 for every half hour the repairer is there. a. Complete the table and show how much it would cost Gustav to have his fridge repaired. **Time** (hours) 0 0.5 1 1.5 2 2.5 3 ------------------ ---- ----- ----- ----- --- ----- --- **Cost** (\$) 55 100 145 b. Draw a graph of this information in the space provided. c. Is there a linear relationship between cost and time? d. Find the gradient of the graph. e. Find the [*y*]{.math.inline}-intercept. f. Find the rule for this graph in the form of [*y* = *mx* + *c*]{.math.inline}. g. In your equation replace [*y*]{.math.inline} with cost and replace [*x*]{.math.inline} with time. h. Use this new equation to find the cost if a repair person takes 4 hours to fix Gustav's fridge.