Final answer:
To have exactly one solution in common with Priya's equation, we need to write another linear equation with the same slope but a different y-intercept, like y = -1/2x + 3.
Step-by-step explanation:
The student is asking to write an equation that has exactly one solution in common with Priya's equation y = -1/2x - 7. To have one solution in common, we need another linear equation that intersects Priya's line at exactly one point.
A simple way to achieve this is by keeping the same slope but changing the y-intercept. So, we could write the new equation as y = -1/2x + b, where b is any number other than -7. For example, y = -1/2x + 3 will intersect Priya's line at exactly one point.