Q. Find the x-Intercept of the Line \( 12x + 11y = 8 \)

Step 1 — Understand what the x‑intercept is. The x‑intercept is the point where the graph crosses the x‑axis. At any point on the x‑axis, the y‑coordinate equals 0. Therefore to find the x‑intercept, set y equal to 0 in the equation of the line.

Step 2 — Substitute y = 0 into the equation. Start with the given line: \(12x + 11y = 8\). Replace y with 0 to obtain:

\(12x + 11(0) = 8\)

Step 3 — Simplify the equation after substitution. Compute 11(0) = 0, so the equation becomes:

\(12x + 0 = 8\)

which simplifies to

\(12x = 8\)

Step 4 — Solve for x. Divide both sides of the equation by 12 to isolate x:

\(x = \dfrac{8}{12}\)

Step 5 — Simplify the fraction. The greatest common divisor of 8 and 12 is 4. Divide numerator and denominator by 4:

\(x = \dfrac{8 \div 4}{12 \div 4} = \dfrac{2}{3}\)

Conclusion — x‑intercept as a point. The x‑intercept is the point with x = \(\tfrac{2}{3}\) and y = 0, i.e.

\(\left(\dfrac{2}{3},\,0\right)\)