This question tests writing equations y=kx for proportional relationships from tables, graphs, contexts, or verbal descriptions, identifying k and defining variables contextually. Proportional equation y=kx: k is constant of proportionality (unit rate, ratio y/x). From table: calculate k from any pair (14/2=7, k=7 gives y=7x), from graph: k=slope (or read y when x=1: if graph through (1,7), k=7), from context: stated rate is k ("$3 per pound" → k=3, equation c=3p where c=cost, p=pounds). Variables: choose meaningful (c for cost, n for number, d for distance) and define in context. For example, context "apples $3/lb" write c=3p (c=cost dollars, p=pounds), k=3 from $/lb rate; or table x:2,4,6 y:10,20,30 find k=10/2=5, write y=5x; or graph through origin with slope 8 write y=8x. The correct equation is f=2.5b with proper k=2.5 and variables f for flour and b for batches. A common error is reversing variables like b=2.5f instead of f=2.5b, wrong form like f=b+2.5 not proportional, or including intercept like f=2.5b+1. To write the equation: (1) identify proportional relationship (context says "2.5 cups per batch"), (2) find k (stated rate of 2.5), (3) choose variables (f for flour, b for batches), (4) write f=2.5b, (5) define variables (f=cups of flour, b=number of batches), (6) verify (b=1, f=2.5×1=2.5, yes✓). Multiple representations: equation f=2.5b matches table of multiples of 2.5, graph with slope 2.5, verbal "2.5 per batch"—all show k=2.5. Mistakes: wrong form (additive), variables reversed, k wrong, undefined variables.

This question tests writing equations y=kx for proportional relationships from tables, graphs, contexts, or verbal descriptions, identifying k and defining variables contextually. Proportional equation y=kx: k is constant of proportionality (unit rate, ratio y/x). From table: calculate k from any pair (14/2=7, k=7 gives y=7x), from graph: k=slope (or read y when x=1: if graph through (1,7), k=7), from context: stated rate is k ("$3 per pound" → k=3, equation c=3p where c=cost, p=pounds). Variables: choose meaningful (c for cost, n for number, d for distance) and define in context. For example, recipe 2 cups flour per batch, write f=2b (f=cups of flour, b=batches), k=2 from cups per batch; or table x:2,4,6 y:10,20,30 find k=10/2=5, write y=5x; or graph through origin with slope 8 write y=8x. The correct equation is f=2b, with k=2 and variables f for flour and b for batches. A common error is reversing like b=2f, using additive f=b+2, or including intercept f=2b+2. To write: (1) identify proportional from "2 cups for each batch," (2) find k=2 as rate, (3) choose f and b, (4) write f=2b, (5) define f as cups and b as batches, (6) verify b=1, f=2. Multiple representations: f=2b matches table multiples of 2, graph slope 2, verbal "2 per batch"—all k=2. Mistakes: reversed variables, wrong form, added constants.

This question tests writing equations y=kx for proportional relationships from tables, graphs, contexts, or verbal descriptions, identifying k and defining variables contextually. Proportional equation y=kx: k is constant of proportionality (unit rate, ratio y/x). From table: calculate k from any pair (14/2=7, k=7 gives y=7x), from graph: k=slope (or read y when x=1: if graph through (1,7), k=7), from context: stated rate is k ("$3 per pound" → k=3, equation c=3p where c=cost, p=pounds). Variables: choose meaningful (c for cost, n for number, d for distance) and define in context. For example: context "apples $3/lb" write c=3p (c=cost dollars, p=pounds), k=3 from $/lb rate; or table x:2,4,6 y:10,20,30 find k=10/2=5, write y=5x; or graph through origin with slope 8 write y=8x. The correct equation is f=(3/2)b, where f is the cups of flour and b is the number of batches, with k=3/2 from 3 cups per 2 batches. A common error is reversing the ratio like f=(2/3)b, reversing variables like b=(3/2)f, or using additive form like f=b+(3/2) instead of multiplicative. To write the equation: (1) identify proportional relationship (context says "3 cups for every 2 batches"), (2) find k (ratio 3/2), (3) choose variables (f for flour, b for batches), (4) write f=(3/2)b, (5) define variables (f=cups of flour, b=number of batches), (6) verify (for b=2, f=(3/2)×2=3, matches✓). Multiple representations: equation f=(3/2)b matches a table with ratios of 3/2, a graph through origin with slope 3/2, and verbal "3 cups per 2 batches"—all show same k=3/2.

This question tests writing equations y=kx for proportional relationships from tables, graphs, contexts, or verbal descriptions, identifying k and defining variables contextually. Proportional equation y=kx: k is constant of proportionality (unit rate, ratio y/x). From table: calculate k from any pair (14/2=7, k=7 gives y=7x), from graph: k=slope (or read y when x=1: if graph through (1,7), k=7), from context: stated rate is k ("$3 per pound" → k=3, equation c=3p where c=cost, p=pounds). Variables: choose meaningful (c for cost, n for number, d for distance) and define in context. For example, in the context of movie tickets at $9 each, write c=9t (c=total cost in dollars, t=number of tickets), where k=9 from the dollars per ticket rate; or table x:2,4,6 y:10,20,30 find k=10/2=5, write y=5x; or graph through origin with slope 8 write y=8x. The correct equation is c=9t, with k=9 and variables c for total cost and t for tickets. A common error is using the wrong form like c=t+9 which is not proportional, or reversing variables like t=9c, or including an intercept like c=9t+9 when it should pass through the origin. To write the equation: (1) identify the proportional relationship from the context "charges $9 per ticket," (2) find k=9 as the stated rate, (3) choose variables c for cost and t for tickets, (4) write c=9t, (5) define c as total cost in dollars and t as number of tickets, (6) verify by substituting t=1, c=9×1=9, which is reasonable. Multiple representations: equation c=9t matches a table where costs are multiples of 9, a graph through origin with slope 9, and the verbal "$9 per ticket"—all show k=9. Mistakes include using additive forms like c=t+9 instead of multiplicative, reversing variables, or adding unnecessary constants.

This question tests writing equations y=kx for proportional relationships from tables, graphs, contexts, or verbal descriptions, identifying k and defining variables contextually. Proportional equation y=kx: k is constant of proportionality (unit rate, ratio y/x). From table: calculate k from any pair (14/2=7, k=7 gives y=7x), from graph: k=slope (or read y when x=1: if graph through (1,7), k=7), from context: stated rate is k ("$3 per pound" → k=3, equation c=3p where c=cost, p=pounds). Variables: choose meaningful (c for cost, n for number, d for distance) and define in context. For example: context "apples $3/lb" write c=3p (c=cost dollars, p=pounds), k=3 from $/lb rate; or table x:2,4,6 y:10,20,30 find k=10/2=5, write y=5x; or graph through origin with slope 8 write y=8x. The correct equation is d=6h, where d is the distance in miles and h is the time in hours, with k=6 from the 6 miles per hour speed. A common error is reversing variables like h=6d instead of d=6h, using a non-proportional form like d=h+6, or adding constants like d=6h+2 when the relationship passes through the origin. To write the equation: (1) identify proportional relationship (context says "constant speed of 6 miles per hour"), (2) find k (stated rate of 6), (3) choose variables (d for distance, h for hours), (4) write d=6h, (5) define variables (d=distance in miles, h=time in hours), (6) verify (for h=2, d=6×2=12, reasonable? yes✓). Multiple representations: equation d=6h matches a table where distances are multiples of 6, a graph through origin with slope 6, and verbal "6 miles per hour"—all show same k=6.

This question tests writing equations y=kx for proportional relationships from tables, graphs, contexts, or verbal descriptions, identifying k and defining variables contextually. Proportional equation y=kx: k is constant of proportionality (unit rate, ratio y/x). From table: calculate k from any pair (14/2=7, k=7 gives y=7x), from graph: k=slope (or read y when x=1: if graph through (1,7), k=7), from context: stated rate is k ("$3 per pound" → k=3, equation c=3p where c=cost, p=pounds). Variables: choose meaningful (c for cost, n for number, d for distance) and define in context. For example, context "apples $3/lb" write c=3p (c=cost dollars, p=pounds), k=3 from $/lb rate; or table x:2,4,6 y:10,20,30 find k=10/2=5, write y=5x; or graph through origin with slope 8 write y=8x. The correct equation is d=55h with proper k=55 and variables d for distance and h for hours. A common error is reversing variables like h=55d instead of d=55h, using wrong form like d=h+55 not proportional, or d=55+h which is additive. To write the equation: (1) identify proportional relationship (context says "55 miles per hour"), (2) find k (stated rate of 55), (3) choose variables (d for distance, h for hours), (4) write d=55h, (5) define variables (d=distance in miles, h=time in hours), (6) verify (substitute h=1, d=55×1=55, reasonable? yes✓). Multiple representations: equation d=55h matches table of multiples of 55, graph through origin with slope 55, verbal "55 mph"—all show same k=55. Mistakes: wrong form (additive d=h+55 not multiplicative), variables reversed, k wrong, forgetting to define variables.

This question tests writing equations y=kx for proportional relationships from tables, graphs, contexts, or verbal descriptions, identifying k and defining variables contextually. Proportional equation y=kx: k is constant of proportionality (unit rate, ratio y/x). From table: calculate k from any pair (14/2=7, k=7 gives y=7x), from graph: k=slope (or read y when x=1: if graph through (1,7), k=7), from context: stated rate is k ("$3 per pound" → k=3, equation c=3p where c=cost, p=pounds). Variables: choose meaningful (c for cost, n for number, d for distance) and define in context. For example, bus 45 miles in 1.5 hours, k=45/1.5=30, write d=30t (d=miles, t=hours); or table x:2,4,6 y:10,20,30 find k=10/2=5, write y=5x; or graph through origin with slope 8 write y=8x. The correct equation is d=30t, with k=30 from calculated rate. A common error is wrong k like d=45t using total without dividing, reversing t=30d, or additive d=t+30. To write: (1) identify proportional from constant rate, (2) find k=30, (3) choose d and t, (4) write d=30t, (5) define d as miles and t as hours, (6) verify t=1.5, d=30×1.5=45. Multiple representations: d=30t matches given point, graph slope 30, verbal "30 mph"—all k=30. Mistakes: wrong k calculation, reversed, added terms.

This question tests writing equations y=kx for proportional relationships from tables, graphs, contexts, or verbal descriptions, identifying k and defining variables contextually. Proportional equation y=kx: k is constant of proportionality (unit rate, ratio y/x). From table: calculate k from any pair (14/2=7, k=7 gives y=7x), from graph: k=slope (or read y when x=1: if graph through (1,7), k=7), from context: stated rate is k ("$3 per pound" → k=3, equation c=3p where c=cost, p=pounds). Variables: choose meaningful (c for cost, n for number, d for distance) and define in context. For example: context "apples $3/lb" write c=3p (c=cost dollars, p=pounds), k=3 from $/lb rate; or table x:2,4,6 y:10,20,30 find k=10/2=5, write y=5x; or graph through origin with slope 8 write y=8x. The correct equation is c=4p, where c is total cost in dollars and p is number of packs, with k=4 from 28/7=4. A common error is using total like c=28p without dividing, additive c=p+28, or reversing p=4c. To write the equation: (1) identify proportional relationship (context says "proportional to the number"), (2) find k (ratio 28/7=4), (3) choose variables (c for cost, p for packs), (4) write c=4p, (5) define variables (c=total cost in dollars, p=number of marker packs), (6) verify (for p=7, c=4×7=28, matches✓). Multiple representations: equation c=4p matches a table with ratio 4, a graph through origin with slope 4, and verbal "$4 per pack"—all show same k=4.

This question tests writing equations y=kx for proportional relationships from tables, graphs, contexts, or verbal descriptions, identifying k and defining variables contextually. Proportional equation y=kx: k is constant of proportionality (unit rate, ratio y/x). From table: calculate k from any pair (14/2=7, k=7 gives y=7x), from graph: k=slope (or read y when x=1: if graph through (1,7), k=7), from context: stated rate is k ("$3 per pound" → k=3, equation c=3p where c=cost, p=pounds). Variables: choose meaningful (c for cost, n for number, d for distance) and define in context. For example: context "apples $3/lb" write c=3p (c=cost dollars, p=pounds), k=3 from $/lb rate; or table x:2,4,6 y:10,20,30 find k=10/2=5, write y=5x; or graph through origin with slope 8 write y=8x. The correct equation is y=(14/4)x, with k=14/4 from the slope through (0,0) and (4,14). A common error is using wrong k like y=14x without dividing, additive form like y=x+(14/4), or reversing like x=(14/4)y. To write the equation: (1) identify proportional relationship (graph through origin), (2) find k (slope=14/4), (3) choose variables (y and x as given), (4) write y=(14/4)x, (5) define variables if needed, (6) verify (for x=4, y=(14/4)×4=14, matches point✓). Multiple representations: equation y=(14/4)x matches graph with slope 14/4, a table with ratio 14/4, and verbal description—all show same k=14/4.

This question tests writing equations y=kx for proportional relationships from tables, graphs, contexts, or verbal descriptions, identifying k and defining variables contextually. Proportional equation y=kx: k is constant of proportionality (unit rate, ratio y/x). From table: calculate k from any pair (14/2=7, k=7 gives y=7x), from graph: k=slope (or read y when x=1: if graph through (1,7), k=7), from context: stated rate is k ("$3 per pound" → k=3, equation c=3p where c=cost, p=pounds). Variables: choose meaningful (c for cost, n for number, d for distance) and define in context. For example, pencils $0.50 each, write m=0.5p (m=cost in dollars, p=pencils), k=0.5 from dollars per pencil; or table x:2,4,6 y:10,20,30 find k=10/2=5, write y=5x; or graph through origin with slope 8 write y=8x. The correct equation is m=0.5p, with k=0.5 and variables m for money and p for pencils. A common error is wrong form like m=p+0.5, reversing p=0.5m, or intercept m=0.5p+0.5. To write: (1) identify from "$0.50 each," (2) find k=0.5, (3) choose m and p, (4) write m=0.5p, (5) define m as dollars and p as pencils, (6) verify p=2, m=1. Multiple representations: m=0.5p matches table like p=1,m=0.5, graph slope 0.5, verbal "half dollar per pencil"—all k=0.5. Mistakes: additive, reversed, extra terms.