If the relationship between y and x is given by the equation y = 1.57 − 0.0407 x, the slope coefficient 0.0407 means this: . for every unit increase in x, y decreases by 1.5293 for every unit increase in x, y increases by 1.5293 for every unit increase in x, y increases by 0.0407 for every unit increase in x, y decreases by 0.0407

The correct answer is for every unit increase in x, y decreases by 0.0407.

Step-by-step explanation:

The equation of the line between x and y is given by y = 1.57 - 0.0407x.

The slope coefficient of this line is -0.0407.

The slope () is negative and thus there is a negative relation between the two variable, i.e. the numerator (y - y1) should decrease as (x - x1) is increasing.

For x = -2 , the value of y is 1.6514.

For x = -1 , the value of y is 1.6107.

For x = 0 , the value of y is 1.57.

For x = 1 , the value of y is 1.5293.

For x = 2 , the value of y is 1.4886.

Thus for every unit increase in x we can see a decrease by 0.0407 in the variable y.