Math  /  Algebra

QuestionUsing a Pattern to Form an Equation
The table shows a representation of the number of miles a car drives over time. \begin{tabular}{|c|c|} \hline Hours, x\boldsymbol{x} & Miles, y\boldsymbol{y} \\ \hline 3 & 195 \\ \hline 4 & 260 \\ \hline 5 & 325 \\ \hline 6 & 390 \\ \hline \end{tabular}
Pattern: Each xx value is multiplied by 65 to get eachy value.
What is the equation for this situation? \square Which could NOT be a point on this table? \square

Studdy Solution

STEP 1

1. The relationship between hours x x and miles y y is linear.
2. Each x x value is multiplied by 65 to obtain the corresponding y y value.
3. We need to find the equation that represents this relationship.
4. We need to determine a point that could not be on the table.

STEP 2

1. Identify the pattern and form the equation.
2. Verify the equation with given data points.
3. Determine a point that could not be on the table.

STEP 3

Identify the pattern: The given pattern states that each x x value is multiplied by 65 to get the corresponding y y value.

STEP 4

Form the equation: Based on the pattern, the equation can be written as: y=65x y = 65x

STEP 5

Verify the equation with given data points: - For x=3 x = 3 , y=65×3=195 y = 65 \times 3 = 195 - For x=4 x = 4 , y=65×4=260 y = 65 \times 4 = 260 - For x=5 x = 5 , y=65×5=325 y = 65 \times 5 = 325 - For x=6 x = 6 , y=65×6=390 y = 65 \times 6 = 390
The equation y=65x y = 65x correctly represents all given data points.

STEP 6

Determine a point that could not be on the table: - A point that does not satisfy y=65x y = 65x cannot be on the table. - For example, consider the point (2,150) (2, 150) : - Calculate y y using the equation: y=65×2=130 y = 65 \times 2 = 130 - Since 150 does not equal 130, the point (2,150) (2, 150) could not be on the table.
The equation for this situation is: y=65x \boxed{y = 65x}
A point that could NOT be on this table is: (2,150) \boxed{(2, 150)}

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