Q. Find the x-intercept of the Line \( 5x + 18y = 4 \)

Answer

Step 1 — Recall what an x-intercept is.

The x-intercept is the point where the graph crosses the x-axis, so the y-coordinate is 0. To find the x-intercept of the line, set \(y = 0\) in the equation and solve for \(x\).
Step 2 — Substitute \(y = 0\) into the equation.

Start with the line equation: \(5x + 18y = 4\). Substitute \(y = 0\) to get \(5x + 18(0) = 4\).
Step 3 — Simplify the equation.

Since \(18(0) = 0\), the equation becomes \(5x = 4\).
Step 4 — Solve for \(x\).

Divide both sides by 5 to isolate \(x\): \(x = \frac{4}{5}\). In decimal form, \(x = 0.8\).
Step 5 — State the x-intercept as an ordered pair.

The x-intercept is \(\left(\frac{4}{5},\,0\right)\), which is the same as \((0.8,\,0)\).

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Homework solver

Set y = 0: 5x = 4, so x = 4/5. The x-intercept is (4/5, 0) or (0.8, 0).

Set y = 0, solve ax = c, so x = c/(provided ≠ 0). The intercept is (c/a, 0).

Set y = 0 and solve 0 = mx + b, so x = -b/m, assuming m ≠ 0. The x-intercept is (-b/m, 0).

If = 0 the equation is by = c. If c ≠ 0 there is no x-intercept; if c = 0 the line is y = 0, which is the x-axis (every point is an x-intercept).

Set x = 0: 18y = 4, so y = 4/18 = 2/9. The y-intercept is (0, 2/9).

Plot the x- and y-intercepts as points on the axes, then draw straight line through them. Two intercepts uniquely determine the line.

Substitute the x value into the original equation with y = 0 to verify the equation holds. For 5x + 18(0) = 4, 5(4/5) = 4, so it checks.

Either form is fine. Use fractions for exact values (4/5), decimals for readability (0.8). Keep fractions when doing algebrto avoid rounding errors.

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