How to find the slope and y intercept to sketch 7 x + 6 y...

The standard form of a linear equation is used for this equation. The standard form of a linear equation is:
${\displaystyle Ax+By=C}$
Where, if at all possible, ${\displaystyle A}$, ${\displaystyle B}$, and ${\displaystyle C}$ are integers, and A is non-negative, and, A, B, and C have no common factors other than 1
${\displaystyle 7x+6y=30}$
The slope of an equation in standard form is: ${\displaystyle m=-\frac{A}{B}}$
Substituting the values from the equation in the problem gives:
${\displaystyle m=-\frac{7}{6}}$
The ${\displaystyle y}$-intercept of an equation in standard form is: ${\displaystyle \frac{C}{B}}$
Substituting the values from the equation in the problem gives:
${\displaystyle \frac{30}{6}=5}$ or ${\displaystyle (0,5)}$