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Match the table, scenario, and graph to the appropriate Linear equation.

A standard Cartesian coordinate plane is presented. The x-axis and y-axis are clearly marked with tick marks, implying a grid system. A straight line is drawn diagonally across the graph, sloping downwards from left to right. The line intersects both axes. The line appears to pass through the point (0, 2), and another point can be estimated roughly as (5, 0). The axes are labeled simply with the standard x and y notations along their respective positions.

x - 2 - 4 - 6 - 8 - 10
y - 25 - 19 - 13 - 7 - 1

Ryan is tracking how much money he has each week.

He started with $60. He spent $5 per week until he had $20 left in the account.


y = 2/3x + 3
y = - 3/2 + 3
y = - 1/3 x + 31
y = - 3x + 31
y = 60x - 5

y = - 5x + 20

y = -5x + 60

y = 3x - 3

1 answer

To find the appropriate linear equation that matches the graph, table, and scenario provided, we can analyze them one by one.

  1. Graph Analysis: The line is sloping downward and passes through points such as (0, 2) and approximately (5, 0). The y-coordinate intercept appears to be 2, and we can calculate the slope using the points provided.

  2. Table: According to the table:

    • When x = 0, y = 25
    • When x = 2, y = 19
    • When x = 4, y = 13
    • When x = 6, y = 7
    • When x = 8, y = 1

    This table data suggests the relationship is not linear with the expected slope calculated as change in y/change in x.

  3. Scenario (Ryan's Money): Ryan starts with $60 and spends $5 per week. His account balance drops consistently, which describes a linear relationship. The scenario concludes with him having $20 left.

Equation for the scenario:

  • Starting point (y-intercept) = $60 when x (weeks) = 0
  • Spending $5 each week indicates the slope = -5
  • This gives us the equation: \[ y = -5x + 60 \]

Thus, the matching equation for Ryan's money is y = -5x + 60.

In conclusion:

  • The graph resembles a line that slopes downward from (0, 2) which aligns well with financial spend-down.
  • The table does not strictly match with the spend trend unless we assess the value ranges.
  • The scenario confirms spending $5, getting us to the linear equation y = -5x + 60.