Now that we have the slope, we can determine the equation of the line. The equation for a line is y = mx + b, where m is the slope and b is the y-intercept.
Since m = 3/4, we can solve for b by plugging in the point (5, 6) for the values of x and y: y = mx + b 6 = (3/4)(5) + b 6 = 15/4 + b 6 – 15/4 = b 9/4 = b
So the equation for the line is: y = (3/4)x + 9/4
Only the (x, y) pair that makes the equation true will be a point on the line described by the equation above. When we substitute the values of x and y from the coordinates in the answer choices, only choice (A) makes the equation true: 9 = (3/4)(9) + 9/4 9 = 27/4 + 9/4 = 36/4 = 9.
The correct answer is choice (A). This question is also easy to solve by simply back-solving the answer choices. ----------
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