Answer:
[tex] y = \frac{2}{3}x + \frac{80}{3} [/tex]
Step-by-step 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:
[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{60 - 40}{50 - 20} = \frac{20}{30} = \frac{2}{3} [/tex]
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:
[tex] y = \frac{2}{3}x + \frac{80}{3} [/tex]
