Question

loren solved the equation \\(10 = \frac{19}{9}(149) + b\\) for \\(b\\) as part of her work to find the equation of a trend line that passes through the points \\((1, 130)\\) and \\((10, 149)\\). what error did loren make?

• she should have solved \\(10 = \frac{9}{19}(149) + b\\) for \\(b\\).
• she should have solved \\(1 = \frac{19}{9}(130) + b\\) for \\(b\\).
• she should have solved \\(149 = \frac{19}{9}(10) + b\\) for \\(b\\).
• she should have solved \\(130 = \frac{9}{19}(1) + b\\) for \\(b\\).

Explanation:

Calculate the slope of the trend line

$$ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{149 - 130}{10 - 1} = \frac{19}{9} $$

Identify the substitution error

Using the slope-intercept form \(y = mx + b\) with the point \((10, 149)\):

$$ 149 = \frac{19}{9}(10) + b $$

Loren incorrectly swapped the \(x\) and \(y\) coordinates by substituting \(x = 149\) and \(y = 10\).

Match with the correct option

Loren should have solved:

$$ 149 = \frac{19}{9}(10) + b $$

Answer:

• She should have solved \(10 = \frac{9}{19}(149) + b\) for \(b\).
• She should have solved \(1 = \frac{19}{9}(130) + b\) for \(b\).
• She should have solved \(149 = \frac{19}{9}(10) + b\) for \(b\). (Correct answer)
• She should have solved \(130 = \frac{9}{19}(1) + b\) for \(b\).