Robert took $32 with him to spend on pizza and games for himself and his friends at Chucky Cheese. The price for each slice of pizza was $4. The price for each game was half the price of a slice of pizza. a) Sketch the graph that represents the situation and label the intercepts with the real world items you are comparing. Use one axis to represent the number of slices of pizza and the other axis to represent the number of games. b) What do the intercepts and the solutions of your graphed function mean in context of the problem? Explain both intercepts.c) If Robert spends his money on both pizza and games, give an example of the number of pizza slices and games Robert can buy if he spends all his money.d) Prove algebraically that you’re above example in C is true.

Answer:Part a) The graph in the attached figurePart b) see the explanationPart c) 6 slices of pizza and 4 gamesPart d) see the explanationStep-by-step explanation:Part a) Letx ----> the number of slices of pizzay ---> the number of gameswe know thatThe price for each slice of pizza was $4The price for each game was half the price of a slice of pizzaso$4(1/2)=$2 ----> the price of each gameThe number of slices of pizza multiplied by $4 plus the number of games multiplied by $2 must be equal to $32so[tex]4x+2y=32[/tex] -----> equation Ausing a graphing toolsee the attached figureThe x-intercept is the point (8,0)The y-intercept is the point (0,16)Part b) What do the intercepts and the solutions of your graphed function mean in context of the problemThe y-intercept -----> that means, the value of y when the value of x is equal to zerosoIn this context, if they spend all money on games, they can play 16 gamesThe x-intercept -----> that means, the value of x when the value of y is equal to zerosoIn this context, if they spend all money on slices of pizza, they can buy 8 slices of pizzaPart c) we know thatIf a ordered pair is a solution of the liner equation , then the ordered pair must satisfy the linear equationExampleThe ordered pair (6,4) lie on the lineVerifyFor x=6 slices of pizza, y=4 gamessubstitute[tex]4(6)+2(4)=32[/tex] [tex]32=32[/tex] ---> is truePart d)x-interceptFor y=0Find the value of x[tex]4x+2(0)=32[/tex][tex]4x=32[/tex][tex]x=8[/tex]The x-intercept is the point (8,0)8 slices of pizza and 0 gamesy-interceptFor x=0[tex]4(0)+2y=32[/tex] [tex]2y=32[/tex] [tex]y=16[/tex]The y-intercept is the point (0,16)0 slices of pizza and 16 games