The slope intercept form of an equation is given by,
[tex]y=mx+c\text{ ---(1)}[/tex]Here, m is the slope and c is the y intercept.
The given equation is,
[tex]y=2\mleft(5x+1\mright)+3\mleft(5x+3\mright)[/tex]Apply distributive property (A[B+C]= AB+BC) in the above equation to make it to the form of equation (1).
[tex]\begin{gathered} y=2\times5x+2\times1+3\times5x+3\times3 \\ y=10x+2+15x+9 \end{gathered}[/tex]Now, combine the like terms.
[tex]\begin{gathered} y=10x+15x+2+9 \\ y=25x+11\text{ ---(2)} \end{gathered}[/tex]Equation (2) is in the form of equation (1).
Therefore, the slope-intercept form of y=2(5x + 1) + 3(5x + 3) is,
y=25x+11.
