Q.Find the value of '$a$' for which the straight lines $3x + 4y = 13$; $2x - 7y = -1$ and $ax - y - 14 = 0$ are concurrent.

The $x$-intercept is found by setting $y=0$; here $3x-1=0$, giving $x=\tfrac13$.

The $x$-intercept is the point where the line crosses the $x$-axis, and every point on the $x$-axis has $y=0$. Substitute $y=0$ into the line:

…

Rewriting $6x-2y+5=0$ in the form $y=mx+c$ gives $y=3x+\tfrac{5}{2}$, so the slope is $m=3$.

Start with the line:

$6x - 2y + 5 = 0.$

Solve for $y$:

$2y = 6x + 5 \;\Rightarrow\; y = 3x + \frac{5}{2}.$ …