find the equation of a trend line using (-7, 43) and (4, -12) as anchor points. y = ?x +
find the equation of a trend line using (-7, 43) and (4, -12) as anchor points. y = ?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}). Let ((x_1, y_1)=(-7, 43)) and ((x_2, y_2)=(4, -12)). So, (m=\frac{-12 - 43}{4 - (-7)}=\frac{-55}{11}=-5).
Step2: Use point - slope form to find the y - intercept (b)
The point - slope form is (y - y_1=m(x - x_1)). We can use one of the points, say ((x_1, y_1)=(-7, 43)) and (m = - 5). Substitute into the formula: (y-43=-5(x + 7)). Expand the right - hand side: (y-43=-5x-35). Add 43 to both sides: (y=-5x - 35 + 43), so (y=-5x+8).
Answer:
The equation of the trend line is (y=-5x + 8), so the coefficient of (x) is (-5) and the y - intercept is (8). Filling in the blanks, we have (y=\boxed{-5}x+\boxed{8})