This question tests identifying independent (input) and dependent (output) variables, writing equations relating them, creating tables, graphing with proper axes, and connecting equation-table-graph representations. Variables: independent is input/chosen first (time t we jog—we control), dependent is output/depends on independent (distance d depends on time—results from independent). Equation: express dependent in terms of independent (d=6t: distance equals 6 times time, dependent d on left, independent t in expression). Table: list independent values (t: 0,1,2,3), calculate dependent using equation (if t=1, d=6×1=6; t=2, d=12; etc.). Graph: independent on x-axis (horizontal: time), dependent on y-axis (vertical: distance), plot ordered pairs ((1,6), (2,12),...), proportional d=kt graphs through origin. For example, distance-time at 65 mph, independent=time t (hours driven), dependent=distance d (miles traveled), equation d=65t, table t:1,2,3 d:65,130,195 (each from 65×t), graph: x-axis time, y-axis distance, points (1,65),(2,130),(3,195) forming line through (0,0) with slope 65 matching equation coefficient. The correct equation is d=6t, showing distance as a function of time at constant speed. Errors like d=t+6 (additive instead of multiplicative) or d=t/6 (inverse) don't match the proportional relationship. Analyzing: (1) identify relationship (distance depends on time at 6 mph), (2) determine independent (time t) and dependent (distance d), (3) write equation (d=6t), (4) create table (t:0,1,2, d:0,6,12), (5) graph (x=t, y=d, plot pairs, line through origin), (6) connect (equation matches table: 6×1=6✓, slope=6✓). Axes convention: independent horizontal (x-axis: time), dependent vertical (y-axis: distance).

This question tests identifying independent (input) and dependent (output) variables, writing equations relating them, creating tables, graphing with proper axes, and connecting equation-table-graph representations. Variables: independent is input/chosen first (hours h worked—we control), dependent is output/depends on independent (money m depends on hours—results from independent). Equation: express dependent in terms of independent (m=5h: money equals 5 times hours, dependent m on left, independent h in expression). Table: list independent values (h: 0,1,2,3), calculate dependent using equation (if h=0, m=0; h=1, m=5; etc.). Graph: independent on x-axis (horizontal: hours), dependent on y-axis (vertical: money), plot ordered pairs ((0,0), (1,5),...), proportional through origin. For example, earning $4 per chore, independent=chores c, dependent=earnings e, equation e=4c, table c:0,1,2 e:0,4,8, graph: x-chores, y-earnings, points (0,0),(1,4),(2,8) line through origin slope 4. The correct ordered pairs are (0,0),(1,5),(2,10),(3,15), with (h,m) format. Errors like reversing pairs ((5,1) instead of (1,5)) or starting without (0,0) for proportional. Analyzing: (1) identify relationship (money depends on hours at $5 each), (2) determine independent (h) and dependent (m), (3) write equation (m=5h), (4) create table (h:0,1,2,3; m:0,5,10,15), (5) graph (x=h, y=m, plot pairs), (6) connect (pairs match equation: 5*1=5✓). Axes convention: independent horizontal (x-axis: hours), dependent vertical (y-axis: money).

Tests identifying independent (input) and dependent (output) variables, writing equations relating them, creating tables, graphing with proper axes, and connecting equation-table-graph representations. Variables: independent is input/chosen first (hours h we rent, items n we buy—we control), dependent is output/depends on independent (total cost c depends on hours, cost depends on items—results from independent). Equation: express dependent in terms of independent (c=3+2h: cost equals 3 plus 2 times hours, dependent c on left, independent h in expression). Table: list independent values (h: 0,1,2,3), calculate dependent using equation (if h=1, c=3+2×1=5; h=2, c=7; etc.). Graph: independent on x-axis (horizontal: hours), dependent on y-axis (vertical: cost), plot ordered pairs ((1,5), (2,7),...), non-proportional due to intercept. In this bike rental example, independent is hours rented (you choose), dependent is total cost (results from choice plus fees), equation c=2h+3, table h:0,1,2 c:3,5,7, graph x=hours, y=cost, line with slope 2 and y-intercept 3. The correct identification is independent: hours rented; dependent: total cost, as in choice B, with others reversing or misusing constants.

This question tests identifying independent (input) and dependent (output) variables, writing equations relating them, creating tables, graphing with proper axes, and connecting equation-table-graph representations. Variables: independent is input/chosen first (time t we travel), dependent is output/depends on independent (distance d depends on time). Equation: express dependent in terms of independent (d=50t: distance equals 50 times time, dependent d on left, independent t in expression). Table: list independent values (t: 0,1,2,3), calculate dependent using equation (if t=0, d=0; t=1, d=50; t=2, d=100; t=3, d=150). Graph: independent on x-axis (horizontal: time), dependent on y-axis (vertical: distance), plot ordered pairs ((0,0), (1,50),...), proportional through origin. Choice B correctly shows the table with d=50t values starting from 0. Errors like A (starting d=50 at t=0, not 0), C (t starts at 1, d starts at 0 mismatch), D (51 instead of 50, calculation error). Analyzing: (1) identify proportional relationship, (2) independent=time t, dependent=distance d, (3) verify table by plugging t into equation, (4) ensure includes t=0 for origin.

This question tests identifying independent (input) and dependent (output) variables, writing equations relating them, creating tables, graphing with proper axes, and connecting equation-table-graph representations. Variables: independent is input/chosen first (snacks s we buy—we control), dependent is output/depends on independent (total cost c depends on snacks plus fixed ticket—results from independent). Equation: express dependent in terms of independent (c=12+2s: cost equals 12 plus 2 times snacks, dependent c on left, independent s in expression). For example, similar to movie with $10 ticket plus $3 drink, independent=drinks d, dependent=cost c, equation c=10+3d, table d:0,1,2 c:10,13,16, graph: x-drinks, y-cost, points (0,10),(1,13) line with y-intercept 10, slope 3. The correct identification is independent s (snacks), dependent c (total cost), as we choose snacks and cost results. Errors include reversing (cost independent, snacks dependent—backward) or misidentifying constants as variables. Analyzing: (1) identify relationship (cost depends on snacks with fixed $12 plus $2 each), (2) determine independent (s: we choose number) and dependent (c: result), (3) write equation (c=12+2s), (4) create table (s:0,1,2; c:12,14,16), (5) graph (x=s, y=c, plot pairs, line through (0,12)), (6) connect (equation matches table✓, slope=2✓). Axes convention: independent horizontal (x-axis: snacks), dependent vertical (y-axis: cost).

Tests identifying independent (input) and dependent (output) variables, writing equations relating them, creating tables, graphing with proper axes, and connecting equation-table-graph representations. Variables: independent is input/chosen first (lawns $n$ mowed, items we buy—we control), dependent is output/depends on independent (money $m$ depends on lawns, cost depends on items—results from independent). Equation: express dependent in terms of independent ($m=4n$: money equals 4 times lawns, dependent $m$ on left, independent $n$ in expression). Table: list independent values ($n$: 0,1,2,3), calculate dependent using equation (if $n=1$, $m=4 \times 1=4$; $n=2$, $m=8$; etc.). Graph: independent on x-axis (horizontal: lawns), dependent on y-axis (vertical: money), plot ordered pairs ($ (1,4), (2,8), \dots $), proportional $m=kn$ graphs through origin. For this lawn mowing example, independent=number of lawns $n$, dependent=money $m$, equation $m=4n$, table $n$:0,1,2 $m$:0,4,8, graph x=lawns, y=money, line through (0,0) with slope 4. The correct equation is $m=4n$ as in choice C, showing dependent $m$ in terms of independent $n$; errors like B reverse variables, A/D use addition instead of multiplication.

Tests identifying independent (input) and dependent (output) variables, writing equations relating them, creating tables, graphing with proper axes, and connecting equation-table-graph representations. Variables: independent is input/chosen first (time t in seconds, periods we measure—we control), dependent is output/depends on independent (distance d depends on time, result depends on period—results from independent). Equation: express dependent in terms of independent (d=7t: distance equals 7 times time, dependent d on left, independent t in expression). Table: list independent values (t: 0,1,2,3), calculate dependent using equation (if t=1, d=7×1=7; t=2, d=14; etc.). Graph: independent on x-axis (horizontal: time), dependent on y-axis (vertical: distance), plot ordered pairs ((1,7), (2,14),...), proportional through origin. In this runner example, independent=time t, dependent=distance d, equation d=7t, table t:0,1,2,3 d:0,7,14,21, graph x=time, y=distance, points (0,0),(1,7),(2,14),(3,21) line with slope 7. The correct ordered pairs are (0,0),(1,7),(2,14),(3,21) as in C (t on x, d on y); errors like A reverse coordinates, B starts at (0,7), D mixes values.

Tests identifying independent (input) and dependent (output) variables, writing equations relating them, creating tables, graphing with proper axes, and connecting equation-table-graph representations. Variables: independent is input/chosen first (weeks w passed, time we wait—we control), dependent is output/depends on independent (height h depends on weeks, result depends on time—results from independent). Equation: express dependent in terms of independent (h=8+3w: height equals 8 plus 3 times weeks, dependent h on left, independent w in expression). Table: list independent values (w: 0,1,2,3), calculate dependent using equation (if w=1, h=8+3×1=11; w=2, h=14; etc.). Graph: independent on x-axis (horizontal: weeks), dependent on y-axis (vertical: height), plot ordered pairs ((1,11), (2,14),...), line with intercept. In this plant growth example, independent=weeks w, dependent=height h, equation h=3w+8, table w:0,1,2 h:8,11,14, graph x=weeks, y=height, line with slope 3 and y-intercept 8. The correct equation is h=3w+8 as in choice A; errors like C reverse variables, D misapplies parentheses, B swaps coefficients.

This question tests identifying independent (input) and dependent (output) variables, writing equations relating them, creating tables, graphing with proper axes, and connecting equation-table-graph representations. Variables: independent is input/chosen first (number of notebooks n we buy—we control), dependent is output/depends on independent (cost c depends on notebooks—results from independent). Equation: express dependent in terms of independent (c=3n: cost equals 3 times notebooks, dependent c on left, independent n in expression). For example, in a similar cost scenario like buying apples at $2 each, independent=number a (apples bought), dependent=cost c (dollars spent), equation c=2a, table a:0,1,2,3 c:0,2,4,6 (each from 2×a), graph: x-axis apples, y-axis cost, points (0,0),(1,2),(2,4),(3,6) forming line through (0,0) with slope 2 matching equation coefficient. The correct choice identifies independent as n (notebooks), dependent as c (cost), with equation c=3n, as we choose notebooks and cost results proportionally. Errors include reversing variables (cost independent, notebooks dependent—backward), or wrong equation (additive like c=n+3 when should be multiplicative c=3n). To analyze: (1) identify relationship (cost depends on notebooks at $3 each), (2) determine independent (n: we choose number bought) and dependent (c: result of buying that many), (3) write equation (c=3n), (4) connect to table or graph (e.g., for n=1, c=3; n=2, c=6, plotting (1,3),(2,6) with slope 3). Axes convention: independent horizontal (x-axis: notebooks), dependent vertical (y-axis: cost).

Tests identifying independent (input) and dependent (output) variables, writing equations relating them, creating tables, graphing with proper axes, and connecting equation-table-graph representations. Variables: independent is input/chosen first (tickets t bought, items n we buy—we control), dependent is output/depends on independent (cost c depends on tickets, cost depends on items—results from independent). Equation: express dependent in terms of independent (c=6t: cost equals 6 times tickets, dependent c on left, independent t in expression). Table: list independent values (t: 0,1,2,3), calculate dependent using equation (if t=1, c=6×1=6; t=2, c=12; etc.). Graph: independent on x-axis (horizontal: tickets), dependent on y-axis (vertical: cost), plot ordered pairs ((1,6), (2,12),...), proportional through origin. For this movie tickets example, independent=tickets t, dependent=cost c, equation c=6t, table t:0,1,2,3 c:0,6,12,18, graph x=tickets, y=cost, line through (0,0) with slope 6. The correct table is t:0,1,2,3 and c:0,6,12,18 as in B; errors like A start at 6 for t=0 (ignores zero), C starts t at 1, D uses wrong rate like 7.