The graph shows a relationship between the size of 18 households and the average amount of time, in hours, each member of the household spends on chores per week. Which equation best models this data set?

A. y = 0.34x + 5.19
B. y = -0.34x - 5.19
C. y = 0.34x - 5.19
D. y = -0.34x + 5.19

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eudora eudora · Answer 1 · 2020-11-18T16:53:07+01:00

Answer:

Option (D)

Step-by-step explanation:

Equation to represent the household expenditure per week will be in the form of,

y = mx + b

Where m = slope of the line

b = y-intercept

From the graph attached,

Since, line of best fit touches the positive side of the y-axis, y-intercept will be positive.

Since, y-values on the graph are decreasing with the increase in the x-values,

Slope of the graph will be negative.

[Slope = [tex]\frac{\text{Rise}}{\text{Run}}[/tex], Since rise of the line is negative and run is positive, slope will be negative]

By these properties equation of the linear graph will be,

y = -0.34x + 5.19

Option (D) will be the correct option.

raphealnwobi raphealnwobi · Answer 2 · 2021-11-25T13:13:59+01:00

The equation that best models this data set is y = -0.34x + 5.19

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the slope of the line and b is the y intercept.

Let y represent the time spent on chores for x household members.

From the graph, the line passes through (3, 4.25) and (8, 2.5). Hence:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-4.25=\frac{2.5-4.25}{8-3}(x-3) \\\\y-4.25=-0.35(x-3)\\\\y=-0.34x+5.2[/tex]

The equation that best models this data set is y = -0.34x + 5.19

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