A taxi company charges a fixed starting fee and a per-mile charge. The cost , in dollars, of a ride that is miles long is given by the equation Which table shows three possible pairs that satisfy this equation?

Solution available with step-by-step explanation

SAT Linear Equations in Two Variables Question 121 | Free SAT Prep | Aniko

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Question 121·Easy·Linear Equations in Two Variables

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A taxi company charges a fixed starting fee and a per-mile charge. The cost $C$ , in dollars, of a ride that is $m$ miles long is given by the equation

C = 2.5m + 3

Which table shows three possible $(m, C)$ pairs that satisfy this equation?

m	C
0	2.5
1	5
4	12.5

m	C
0	0
1	2.5
4	10

For equation-and-table questions, substitute the table’s $m$ values into the equation and compute the matching $C$ values (or plug the $(m, C)$ pairs into the equation to see if both sides are equal). You usually only need to check one or two rows to eliminate wrong tables quickly, then confirm with a third value if needed; this is much faster and less error-prone than trying to reason about all choices at once or graphing during the test.

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Start with the fixed cost

What is the cost $C$ when $m = 0$ ? Plug $m = 0$ into $C = 2.5m + 3$ and see which tables have that value in the row where $m = 0$ .

Check another point

Now plug $m = 1$ into $C = 2.5m + 3$ . Which tables give that same $C$ value when $m = 1$ ?

Verify all three rows

For any table that still seems possible, also check the row where $m = 4$ by plugging $m = 4$ into the equation. The correct table must match the equation for all three $(m, C)$ pairs.

Desmos Guide

Enter the equation

In Desmos, type the equation as y = 2.5x + 3. This graphs the cost $C$ (as $y$ ) versus miles $m$ (as $x$ ).

Use a table to find exact values

Add a table in Desmos (click the "+" then "Table"), and enter $x$ -values $0$ , $1$ , and $4$ in the first column. Desmos will automatically fill in the corresponding $y$ -values from the equation. These $y$ -values are the $C$ values that go with each $m$ ; compare them to the answer choice tables to see which one matches all three pairs.

Step-by-step Explanation

Interpret the equation

The equation $C = 2.5m + 3$ tells you how the taxi fare is calculated:

$m$ is the number of miles.
$C$ is the total cost in dollars.
$2.5$ is the cost per mile.
$3$ is the fixed starting fee (the cost when $m = 0$ ).

Compute the cost for the given mile values

Use the equation to find $C$ for $m = 0$ , $m = 1$ , and $m = 4$ .

For $m = 0$ : $C = 2.5(0) + 3 = 0 + 3 = 3$ .
For $m = 1$ : $C = 2.5(1) + 3 = 2.5 + 3 = 5.5$ .
For $m = 4$ : $C = 2.5(4) + 3 = 10 + 3 = 13$ .

Match the computed pairs to a table

The three $(m, C)$ pairs that satisfy the equation are $(0, 3)$ , $(1, 5.5)$ , and $(4, 13)$ . Look through the answer choices and find the table that shows exactly these three pairs. That table is option A:

m	C
0	3
1	5.5
4	13

Study Hints

Hints

Click me!

Start with the fixed cost

What is the cost $C$ when $m = 0$ ? Plug $m = 0$ into $C = 2.5m + 3$ and see which tables have that value in the row where $m = 0$ .

Check another point

Now plug $m = 1$ into $C = 2.5m + 3$ . Which tables give that same $C$ value when $m = 1$ ?

Verify all three rows

For any table that still seems possible, also check the row where $m = 4$ by plugging $m = 4$ into the equation. The correct table must match the equation for all three $(m, C)$ pairs.

Desmos Guide

Enter the equation

In Desmos, type the equation as y = 2.5x + 3. This graphs the cost $C$ (as $y$ ) versus miles $m$ (as $x$ ).

Use a table to find exact values

Step-by-step Explanation

Interpret the equation

The equation $C = 2.5m + 3$ tells you how the taxi fare is calculated:

$m$ is the number of miles.
$C$ is the total cost in dollars.
$2.5$ is the cost per mile.
$3$ is the fixed starting fee (the cost when $m = 0$ ).

Compute the cost for the given mile values

Use the equation to find $C$ for $m = 0$ , $m = 1$ , and $m = 4$ .

For $m = 0$ : $C = 2.5(0) + 3 = 0 + 3 = 3$ .
For $m = 1$ : $C = 2.5(1) + 3 = 2.5 + 3 = 5.5$ .
For $m = 4$ : $C = 2.5(4) + 3 = 10 + 3 = 13$ .

Match the computed pairs to a table

m	C
0	3
1	5.5
4	13

Strategy

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Desmos Guide

Step-by-step Explanation

Study Hints

Strategy

Hints

Desmos Guide

Step-by-step Explanation