Answer: The required slope-intercept form of the given linear equation is
\(y=4x-14.\)
Step-by-step explanation: We are given to write the following linear equation in slope-intercept form :
\(y+2=4(x-3)~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\)
We know that
the slope-intercept form of a straight line is written as
\(y=mx+c,\)
where 'm' is the slope and 'c' is the y-intercept of the line.
From equation (i), we have
\(y+2=4(x-3)\\\\\Rightarrow y+2=4x-12\\\\\Rightarrow y=4x-12-2\\\\\Rightarrow y=4x-14.\)
Thus, the required slope-intercept form of the given linear equation is
\(y=4x-14,\) where slope, m = 4 and y-intercept, c = -14.
