To determine which of the given equations represents a line that goes through the points (9, 3) and (11, 17), we first need to find the slope of the line that connects these two points.
The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Plugging in the coordinates of the points (9, 3) and (11, 17):
- \( x_1 = 9, y_1 = 3 \)
- \( x_2 = 11, y_2 = 17 \)
Calculating the slope:
\[ m = \frac{17 - 3}{11 - 9} = \frac{14}{2} = 7 \]
Now that we have the slope of the line (7), we can use point-slope form to write the equation of the line. The point-slope form is:
\[ y - y_1 = m(x - x_1) \]
Using the point (9, 3) and the slope of 7, the equation becomes:
\[ y - 3 = 7(x - 9) \]
Now we can check the other options given:
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\( y - 3 = 7(x - 9) \): This is correct; it is the equation we derived.
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\( y + 10 = 7(x + 10) \): We can check this by solving for y: \[ y + 10 = 7x + 70 \implies y = 7x + 60 \] This line does not pass through (9, 3) or (11, 17).
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\( y - 11 = -7(x - 17) \): Check by solving for y: \[ y - 11 = -7x + 119 \implies y = -7x + 130 \] This line also does not pass through (9, 3) or (11, 17).
Only the first option represents the correct line through the given points. Thus, the only correct equation is:
\( y - 3 = 7(x - 9) \).
Only one of the provided options is correct, so the statement "Two of these are correct" is inaccurate.