Question

Write the equation of the line that connects each set of data points.

Answer 1

`y = (2)/(3)x + (80)/(3)`

Explanation:

To write this equation in slope-intercept form, find the slope (m) and y-intercept (b).

Using the coordinates of two points, (20, 40) and (50, 60), thus:

`slope (m) = (y_2 - y_1)/(x_2 - x_1) = (60 - 40)/(50 - 20) = (20)/(30) = (2)/(3)`

m = ⅔.

Substitute the coordinates of any of the points, say (20, 40) and the slope value in y = mx + b, to find the value of the y-intercept, b.

Thus, substituting x = 20, y = 40, and m = ⅔ into y = mx + b.

40 = (⅔)(20) + b

40 = 40/3 + b

Subtract 40/3 from each side

40 - 40/3 = b

(120 - 40)/3 = b

80/3 = b

Substitute m = ⅔, and b = 80/3 into y = mx + b.

Thus, the equation of the line that connects each set of data points would be:

`y = (2)/(3)x + (80)/(3)`