Final answer:
To find an equation of the line passing through the point (-1, 7) and parallel to the line through points (-3, 4) and (4, -1), calculate the slope between these points and use the point-slope form with the new point to derive the equation y = (-5/7)x + 12.
Step-by-step explanation:
The correct answer is option Mathematics. To find an equation of the line that passes through the point (−1, 7) and is parallel to the line joining the points (−3, 4) and (4, −1), first, we need to calculate the slope of the line through those two points.
The slope, m, is obtained by the formula m = (y2 - y1) / (x2 - x1), which in this case yields m = (−1 - 4) / (4 - (−3)) = (−5) / 7. Since parallel lines have equal slopes, our new line will have the same slope of −5/7. The point-slope form of the equation of a line is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Substituting our point (−1, 7) and the slope −5/7, we get y - 7 = (−5/7)(x - (−1)). Simplifying, we find the equation of the line to be y = (−5/7)x + 12.