Intercepts of a straight line: For the line through points (−2, 8) and (5, 7), determine which axes it cuts.

Introduction / Context:
Given two points, we can write the equation of the line and test intercepts by checking where it meets the x- and y-axes. This reinforces slope-intercept concepts and evaluating linear equations at y = 0 or x = 0.

Given Data / Assumptions:

• Points: A(−2, 8) and B(5, 7).
• We want to know whether the line meets the x-axis, the y-axis, both, or neither.

Concept / Approach:
Compute slope m = (y2 − y1)/(x2 − x1). Use point-slope form to obtain the equation. Then find the y-intercept by setting x = 0, and the x-intercept by setting y = 0.

Step-by-Step Solution:

Verification / Alternative check:
Because the slope is finite and not zero, and the line's equation yields finite intercepts at both substitutions, the line crosses both axes exactly once.

Why Other Options Are Wrong:
It is not parallel to either axis (slope is −1/7), so it cannot avoid both axes nor cut only one axis.

Common Pitfalls:
Sign mistakes when applying point-slope form or solving for intercepts can lead to wrong conclusions about which axes are cut.

Final Answer:
cuts both the axes