To find the new function, we need to modify the slope and the y-intercept. The new function will be y = 2mx + (b + 3), resulting in a steeper line shifting upwards on the y-axis.
The slope of a linear function represents the rate of change between the x-axis and y-axis. In this case, the student is given a starting point at (-0.5, 0) on the x-axis and (0, 1) on the y-axis. To find the new function, we need to multiply the slope by 2 (since the slope will be multiplied by 2) and increase the y-value of the y-intercept by 3 units.
Using these modifications, the new function will be:
y = 2mx + (b + 3).
Graphically, this will result in the line shifting upwards on the y-axis and becoming steeper.
Based on the given options, the graph that best represents the new function would show a steeper line passing through the point (-0.5, 0) and (0, 4).