Final answer:
To find another point on the line that goes through the points (-4, 6) and (10, -1), calculate the slope using the formula m = (y2 - y1) / (x2 - x1), then use the slope-intercept form y = mx + b and one of the given points to find the equation of the line. Finally, substitute the x-coordinate of one of the given answer choices into the equation to find the corresponding y-coordinate. Therefore, the correct answer is A. (2, 7).
Step-by-step explanation:
To find another point on the line that goes through the points (-4, 6) and (10, -1), we can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.
First, calculate the slope using the formula m = (y2 - y1) / (x2 - x1). In this case, the coordinates are (-4, 6) and (10, -1). Plugging in the values, we get m = (-1 - 6) / (10 - (-4)) = -7 / 14 = -1/2.
Next, use the slope-intercept form and one of the given points to find the equation of the line. Using the point (-4, 6) and the slope -1/2, we have y = (-1/2)x + b. Plugging in the values, we can solve for b: 6 = (-1/2)(-4) + b. Solving for b, we get b = 8.
Therefore, the equation of the line is y = (-1/2)x + 8. Finally, substitute the x-coordinate of one of the given answer choices into the equation to find the corresponding y-coordinate. For example, when x = 2, y = (-1/2)(2) + 8 = 7. Therefore, the correct answer is A. (2, 7).