Final answer:
The student's question is about determining which option correctly represents the line with the equation y = -5x + 4. None of the options provided have points that, when used to calculate the slope or test the equation, match both the slope and y-intercept of the equation y = -5x + 4.
Step-by-step explanation:
The student is asking about the slope-intercept form of a line, which is written as y = mx + b, where m is the slope and b is the y-intercept. To find which option has an equation of y = -5x + 4, we can calculate the slopes of the lines given by the points in each option and compare them to the slope in the question (-5).
Option 2: Using points (2, -14) and (4, -24), the slope is (y2 - y1) / (x2 - x1) = (-24 - (-14)) / (4 - 2) = -10 / 2 = -5, which matches the slope of -5 from the equation y = -5x + 4. Moreover, if we insert x = 2 into the equation y = -5x + 4, we get y = -5(2) + 4 = -10 + 4 = -6, which does not match the y-value of the point (2, -14). Therefore, the line through points (2, -14) and (4, -24) cannot have the equation y = -5x + 4, because the y-values do not match. The error in y-values indicates that Option 2 is not the correct answer.
After evaluating all options, none of the given pairs of points result in a consistent y-value when plugged into the equation y = -5x + 4. Therefore, none of the provided options correctly represents the line with the equation y = -5x + 4.