Given the system of inequalities: 4x – 5y < 1One-halfy – x < 3Which shows the given inequalities in slope-intercept form?y < Four-fifthsx – One-fifthy < 2x + 6y > Four-fifthsx – One-fifthsy < 2x + 6y > Negative four-fifthsx + One-fifthy > 2x + 6

Answer:[tex]4x-5y<1[/tex] slope intercept form is option 3 - [tex]y>\frac{4x}{5}-\frac{1}{5}[/tex][tex]\frac{1}{2}y-x<3[/tex] slope intercept form is option 4 - [tex]y<2x+6[/tex]Step-by-step explanation:Given : The system of inequalities [tex]4x-5y<1[/tex] and [tex]\frac{1}{2}y-x<3[/tex]To find : Which shows the given inequalities in slope-intercept form?Solution : The slope intercept form is [tex]y=mx+b[/tex] where m is the slope and b is y-intercept.First inequality is [tex]4x-5y<1[/tex]Now we take y to one side by subtracting 4x both side,[tex]-5y<1-4x[/tex]Divide both side by 5,[tex]-y<\frac{1-4x}{5}[/tex]Multiply both side by -1,[tex]y>-\frac{1-4x}{5}[/tex][tex]y>\frac{4x-1}{5}[/tex][tex]y>\frac{4x}{5}-\frac{1}{5}[/tex]So, Option 3 is correct.Second inequality is [tex]\frac{1}{2}y-x<3[/tex]Now we take y to one side by adding x both side,[tex]\frac{1}{2}y<3+x[/tex]Multiply both side by 2,[tex]y<2(3+x)[/tex][tex]y<6+2x[/tex][tex]y<2x+6[/tex]So, Option 4 is correct.