Final answer:
The measure of the angle that the line makes with the positive x-axis in radians is tan^-1(7/8).
Step-by-step explanation:
The line y=(7)/(8)x passes through the origin (0,0) in the xy-plane. To find the measure of the angle that the line makes with the positive x-axis in radians, we can use the formula: tan(θ) = slope. In this case, the slope is 7/8. To find the measure of the angle, we can take the inverse tangent (tan-1) of the slope. Therefore, the measure of the angle in radians is tan-1(7/8).