Final answer:
The equation of the dilated line m is 2x + y = 1/4, maintaining the same slope as line h, but with the y-intercept divided by the scale factor of 4.
Step-by-step explanation:
The question asks what the equation of line m is if it is a dilation of line h with the equation 2x + y = 1, using a scale factor of 4 with respect to the origin. In this situation, a dilation by a scale factor of 4 means that the coordinates of every point on line m will be 4 times the coordinates of the corresponding points on line h. To find the equation of line m, we can use the concept of slope (m in the slope-intercept form of a line's equation, y = mx + b).
To maintain the same slope after the dilation, the coefficient of x (which is the slope of line h) must remain the same. Hence, we keep the slope at 2. To find the new y-intercept, we divide the constant term in the equation of line h by the scale factor. Therefore, the equation of line m will be 2x + y = 1/4.