Question

1. jasper hikes 4 miles per hour. the function rule that represents this situation is 4x, where x is the number of hours. make a table to find how many hours he has hiked when he has gone 8, 12, and 20 miles. then graph the function.
2. jamie has 3 game tickets more than twice her brother’s game tickets. the function rule, 3x + 2 where x is her brother’s tickets, can be used to find jamie’s number of tickets. make a table of values that show how many tickets jamie has when her brother has 40, 50, and 60 tickets. then graph the function.

Explanation:

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Problem 11

Step1: Rearrange for hours $x$

Given $y=4x$, solve for $x$: $x=\frac{y}{4}$

Step2: Calculate $x$ for $y=8$

$x=\frac{8}{4}=2$

Step3: Calculate $x$ for $y=12$

$x=\frac{12}{4}=3$

Step4: Calculate $x$ for $y=20$

$x=\frac{20}{4}=5$

Step5: Fill the table

Hours ($x$)	$4x$	Miles ($y$)
3	$4*3$	12
5	$4*5$	20

Step6: Graph key points

Plot points $(2,8)$, $(3,12)$, $(5,20)$ on the axes (x=hours, y=miles) and draw a straight line through them (including the origin $(0,0)$).

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Problem 12

Step1: Substitute $x=40$ into $3x+2$

$y=3(40)+2=120+2=122$

Step2: Substitute $x=50$ into $3x+2$

$y=3(50)+2=150+2=152$

Step3: Substitute $x=60$ into $3x+2$

$y=3(60)+2=180+2=182$

Step4: Fill the table

Jamie's Brother's Tickets ($x$)	$3x+2$	Jamie's Tickets ($y$)
50	$3*50+2$	152
60	$3*60+2$	182

Step5: Graph key points

Plot points $(40,122)$, $(50,152)$, $(60,182)$ on the axes (x=brother's tickets, y=Jamie's tickets) and draw a straight line through them.

Answer:

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Problem 11

Completed Table:

Hours ($x$)	$4x$	Miles ($y$)
3	$4*3$	12
5	$4*5$	20

Graph: A straight line passing through $(0,0)$, $(2,8)$, $(3,12)$, $(5,20)$ with x-axis (Hours) and y-axis (Distance in miles).

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Problem 12

Completed Table:

Jamie's Brother's Tickets ($x$)	$3x+2$	Jamie's Tickets ($y$)
50	$3*50+2$	152
60	$3*60+2$	182

Graph: A straight line passing through $(40,122)$, $(50,152)$, $(60,182)$ with x-axis (Jamie's Brother's Tickets) and y-axis (Jamie's Tickets).