Final answer:
The given equation y = 2x + 3 does not represent the line passing through the points (-2, 7) and (5, -14), as substituting the x-values from these points into the equation results in y-values that do not match those of the points.
Step-by-step explanation:
The question is asking whether the equation y = 2x + 3 represents the straight line that passes through the points (-2, 7) and (5, -14). To determine if this is the correct equation, we need to check whether these points satisfy the equation. Start by plugging in the x-values of the given points into the equation to see if the resulting y-values match those in the points.
For the point (-2, 7), we substitute x with -2:
y = 2(-2) + 3 = -4 + 3 = -1.
This does not match the y-value of 7 that we have in our point, thus the point (-2, 7) does not lie on the line defined by the equation y = 2x + 3.
Similarly, for the point (5, -14), substitute x with 5:
y = 2(5) + 3 = 10 + 3 = 13.
This does not match the y-value of -14 that we have in our point, indicating that the point (5, -14) also does not lie on the line y = 2x + 3. Hence, the given equation does not represent the straight line passing through the points (-2,7) and (5, -14).