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.
Answer:
y >_4/5x – 1/5 ; greater than or equal to symbol next to the y
y < _2x + 6; less than or equal to symbol next to the y
Step-by-step explanation:
