Final answer:
To find the equation of the line through the points (-5, 1) and (7, -9), we calculate the slope which is -5/6. We use one point to find the y-intercept and the resulting equation is y = (-5/6)x + (31/6). None of the provided options match this equation.
Step-by-step explanation:
Finding the Equation of a Line Through Two Points
To find the equation of a line that passes through two points, first, we need to determine the slope of the line. The slope, denoted as m, is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. Applying this formula to the points (-5, 1) and (7, -9), we get m = (-9 - 1) / (7 - (-5)) = -10 / 12 = -5 / 6.
Using the slope, we can now write the slope-intercept form of the equation, which is y = mx + b. To find b, the y-intercept, we can substitute the slope and the coordinates of one of the points into the equation. For example, using point (-5, 1), we have 1 = (-5/6)(-5) + b, which gives us b = 1 - (-25/6), resulting in b = 1 + 25/6 = 31/6.
Hence, the equation of the line in slope-intercept form is y = (-5/6)x + (31/6). This equation, however, does not match any of the options provided in the original question.
It seems there might have been either a calculation error in the provided options or a typo. None of the options a) y = -2x - 11, b) y = 2x - 11, c) y = -2x + 11, or d) y = 2x + 11 correspond to the equation derived from the given points.