Question

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the rate at which money is earned per lawn mowed, we can calculate the ratio of money earned to lawns mowed for each data point:

For x=7, y=294, ratio = 294/7 ≈ 42
For x=6, y=252, ratio = 252/6 = 42
For x=2, y=84, ratio = 84/2 = 42
For x=9, y=378, ratio = 378/9 ≈ 42
For x=3, y=126, ratio = 126/3 = 42

The rate at which money is earned per lawn mowed is approximately $42.

Answer 2

Match the equation type with the correct equation for this table

Standard form

Answer 3

[AI-generated answer — Bot GPT 3.5]

The standard form of a linear equation is given by:

Ax + By = C

To find the standard form equation that matches the given table, we need to substitute the values for x, y, and solve for the coefficients A, B, and C.

Given the data points:
(7, 294)
(6, 252)
(2, 84)
(9, 378)
(3, 126)

We can plug in the values for x and y into the general form equation and solve for A, B, and C:

For the point (7, 294):
7A + B = 294

For the point (6, 252):
6A + B = 252

For the point (2, 84):
2A + B = 84

For the point (9, 378):
9A + B = 378

For the point (3, 126):
3A + B = 126

By solving these equations simultaneously, we can determine the values of A, B, and C in standard form.

Answer 4

so what is the answer in standard form

Answer 5

[AI-generated answer — Bot GPT 3.5]

To find the standard form equation that matches the given table, we can solve the system of equations formed by the data points:

7A + B = 294
6A + B = 252
2A + B = 84
9A + B = 378
3A + B = 126

Subtracting the first equation from the second gives -A = -42 or A = 42. Substituting this value back into the first equation gives:

7(42) + B = 294
294 + B = 294
B = 294 - 294
B = 0

Therefore, the standard form of the linear equation for the given table is:
42x + 0y = 294
42x = 294

So, the standard form equation for this table is:
42x = 294

Answer 6

what is the slope

Answer 7

[AI-generated answer — Bot GPT 3.5]

The standard form equation you found is 42x = 294, which can also be written as y = (294/42)x or y = 7x.

The slope of a linear equation in the form y = mx + b is represented by the coefficient of x, which in this case is 7.

Therefore, the slope of the standard form equation for the given table is 7.

Answer 8

You need to subtract y2-y1

Then divide it with x2-x1

Answer 9

[AI-generated answer — Bot GPT 3.5]

I apologize for the oversight. Let's calculate the slope using the formula:

slope = (y₂ - y₁) / (x₂ - x₁).

Using the data points (7, 294) and (6, 252), we have:
slope = (252 - 294) / (6 - 7)
slope = (-42) / (-1)
slope = 42

Therefore, the correct slope of the linear equation for the given table is 42. Thank you for pointing out the error.

Answer 10

so now we know that the slope is 42 so what is the standard form

Answer 11

[AI-generated answer — Bot GPT 3.5]

Since we know the slope of the linear equation from the given data points is 42, we can use the slope-intercept form of a linear equation, y = mx + b, to find the equation in standard form, Ax + By = C.

Given that the slope (m) is 42 and the data points (7, 294), we can substitute these values into the equation to solve for the y-intercept (b):

y = mx + b
294 = 42(7) + b
294 = 294 + b
b = 294 - 294
b = 0

Now that we have found the y-intercept (b = 0), we can represent the equation in slope-intercept form as: y = 42x

To convert this to standard form, we rearrange the equation:
-y + 42x = 0
y = 42x

The standard form of the linear equation matching the data points in the given table is: -y + 42x = 0.