find the equation of a trend line using (12, 15) and (20, 31) as anchor points.\ny = ?x +
find the equation of a trend line using (12, 15) and (20, 31) as anchor points.\ny = ?x +
Answer
Explanation:
Step1: Calculate the slope (m)
The formula for slope between two points ((x_1, y_1)) and ((x_2, y_2)) is (m = \frac{y_2 - y_1}{x_2 - x_1}). Using ((12, 15)) as ((x_1, y_1)) and ((20, 31)) as ((x_2, y_2)), we have: (m=\frac{31 - 15}{20 - 12}=\frac{16}{8} = 2)
Step2: Find the y-intercept (b)
Use the point - slope form (y - y_1=m(x - x_1)) or substitute (x), (y) and (m) into (y=mx + b). Let's use (y=mx + b) with the point ((12,15)) and (m = 2). Substitute (x = 12), (y = 15) and (m=2) into (y=mx + b): (15=2\times12 + b) (15 = 24 + b) Subtract 24 from both sides: (b=15 - 24=- 9)
Answer:
The equation of the trend line is (y = 2x-9), so the slope is (2) and the y - intercept is (-9). Filling in the blanks, we have (y=\boxed{2}x+\boxed{-9})