Answer
The given statement is true.
Work Step by Step
Consider the given linear equation:
\[5x+6y-30=0\] (1)
Rearrange the equation (1) in the slope–intercept form:\[y=mx+c\]
\[\begin{align}
& 5x+6y-30+30=30 \\
& 5x+6y=30 \\
& 5x+6y-5x=30-5x \\
& 6y=30-5x
\end{align}\]
Dividing both sides by 6 we get,
\[\begin{align}
& y=\frac{30}{6}-\frac{5}{6}x \\
& =5-\frac{5}{6}x
\end{align}\]
Rearranging further:
\[y=-\frac{5}{6}x+5\]
Hence, the slope–intercept form of the given equation is\[y=-\frac{5}{6}x+5\].
Compare this equation to the standard slope intercept form equation of a straight line to get the value of the slope and y intercept.
\[\begin{align}
& m=\frac{-5}{6} \\
& b=5 \\
\end{align}\]
Now, consider the slope–intercept form obtained for the given equation:
\[y=-\frac{5}{6}x+5\]
