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Given the table for x, lawns mowed, and y, money earned:

x - # of lawns mowed 7 6 2 9 3
y - $ earned 294 252 84 378 126
Match the equation type with the correct equation for this table.

Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Standard form
Slope-intercept form
Point-Slope form

Answers:
y = -42x + 2
y = 42x
y = x + 42
6x - 252y = 42
2x + 84y = 42
42x - y = 0
(y - 84) = 42 (x - 2)
(y + 126) = 42(x + 3)
(y - 7) = 42(x - 294)

1 answer

To match the correct equations to the respective forms from the given table of lawns mowed and money earned, we need to analyze the relationships.

  1. Slope-intercept form: The slope-intercept form of a linear equation is given as \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

    From the data, we calculate the slope \(m\). We can take two points, for example (2, 84) and (6, 252): \[ m = \frac{252 - 84}{6 - 2} = \frac{168}{4} = 42 \] Now, using the point (2, 84): \[ y - 84 = 42(x - 2), \] which is the Point-Slope form of the equation.

    Corresponding answer: \( (y - 84) = 42(x - 2) \)

  2. Standard form: This takes the form of \(Ax + By = C\). From the slope we found earlier (42), let's use the line equation \(y = 42x\) in standard form: \[ -42x + y = 0 \quad \text{or} \quad 42x - y = 0 \] Both forms are equivalent, but we can use one of them.

    Corresponding answer: \(42x - y = 0\)

  3. Other forms: The other equations provided do not match standard or slope-intercept forms correctly based on the slope and values calculated from the data.

Combining this information, we have:

  • Slope-intercept form: \(y = 42x\)
  • Standard form: \(42x - y = 0\)
  • Point-Slope form: \( (y - 84) = 42(x - 2) \)

Therefore, in the format requested:

Put responses in the correct input to answer the question.

  • Standard form: \(42x - y = 0\)
  • Slope-intercept form: \(y = 42x\)
  • Point-Slope form: \((y - 84) = 42(x - 2)\)