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Find a line of fit using (10,0.75) and (15,0.69). Enter the correct values to the nearest hundredth in the boxes.

Find a line of fit using (10,0.75) (10,0.75) and (15,0.69) (15,0.69) .\newlineEnter the correct values to the nearest hundredth in the boxes.

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Full solution

Q. Find a line of fit using (10,0.75) (10,0.75) and (15,0.69) (15,0.69) .\newlineEnter the correct values to the nearest hundredth in the boxes.
  1. Calculate slope: First, let's calculate the slope mm of the line using the formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}. So, m=0.69−0.7515−10=−0.065=−0.012m = \frac{0.69 - 0.75}{15 - 10} = \frac{-0.06}{5} = -0.012.
  2. Use point-slope form: Now, we'll use the point-slope form to find the equation of the line. We can use either point, but let's use (10,0.75)(10, 0.75). The point-slope form is y−y1=m(x−x1)y - y_1 = m(x - x_1). So, y−0.75=−0.012(x−10)y - 0.75 = -0.012(x - 10).
  3. Simplify equation: Next, we'll simplify the equation by distributing the slope on the right side. y−0.75=−0.012x+0.12y - 0.75 = -0.012x + 0.12.
  4. Add 0.750.75: Then, we'll add 0.750.75 to both sides to get yy by itself.\newliney=−0.012x+0.12+0.75y = -0.012x + 0.12 + 0.75.
  5. Combine like terms: Finally, we'll combine like terms to get the final equation. y=−0.012x+0.87y = -0.012x + 0.87.

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