Q. Find the x-intercept of the line \(10x + 14y = -18\).

Understand what the x-intercept means.

The x-intercept is the point where the graph of the line crosses the x-axis. Every point on the x-axis has y = 0, so to find the x-intercept we set y equal to 0 in the equation of the line.

Substitute y = 0 into the given equation.

The line is given by

\[10x + 14y = -18\]

Set y = 0 and substitute:

\[10x + 14(0) = -18\]

Simplify the equation after substitution.

Because 14(0) = 0, the equation becomes

\[10x = -18\]

Solve for x.

Divide both sides of the equation by 10 to isolate x:

\[x = \frac{-18}{10}\]

Simplify the fraction and (optionally) convert to a decimal.

Reduce the fraction by dividing numerator and denominator by 2:

\[x = \frac{-9}{5}\]

As a decimal, this is

\[x = -1.8\]

State the x-intercept as a point.

The x-intercept is the point on the x-axis corresponding to this x-value, so the x-intercept is

\[\left(-\frac{9}{5},\,0\right)\quad\text{(which is the same as }\left(-1.8,\,0\right)\text{)}.

Quick check (verification).

Substitute x = -9/5 and y = 0 back into the original equation:

\[10\left(-\frac{9}{5}\right) + 14(0) = 10\cdot\left(-\frac{9}{5}\right) = -18,\]

which matches the right-hand side, confirming the result is correct.