Linear equation forms. Game on.

Point-slope form is $y - y_{1} = m(x - x_{1})\textsf{.}$ The slope is $m = 2$ and the point is $(3, 4)\textsf{,}$ so the equation is $y - 4 = 2(x - 3)\textsf{.}$

In slope-intercept form $y = mx + b$, the coefficient of $x$ is the slope. Here $m = 3$.

In slope-intercept form $y = mx + b$, the constant term $b$ is the $y$-intercept. Here $b = 7$.

Solve for $y$: $2y = -4x + 10$, so $y = -2x + 5$ and $m = -2$.

Slope-intercept form is $y = mx + b\textsf{.}$ The slope is $m = 3$ and the $y$-intercept is $b = 5\textsf{,}$ so the equation is $y = 3x + 5\textsf{.}$

Substitute the point: $5 = 3(1) + b$, so $b = 5 - 3 = 2$.

Subtract $y$ and $5$ from both sides of $y = 2x + 5$ to get $-5 = 2x - y$, or $2x - y = -5\textsf{.}$

Set $y = 0$: $2x = 12$, so $x = 6$.