Final answer:
The inequalities in slope-intercept form are y > (4/5)x - 1/5 and y < 2x + 6.
Step-by-step explanation:
The given system of inequalities is:
4x – 5y < 1
1/2y – x < 3
To write these inequalities in slope-intercept form, we need to isolate y on one side of each equation. The slope-intercept form of an equation is y = mx + b where m is the slope and b is the y-intercept.
For the first inequality, rearrange it to get:
-5y < -4x + 1
y > (4/5)x - 1/5
So, the first given inequality in slope-intercept form is y > (4/5)x - 1/5.
For the second inequality, rearrange it to get:
1/2y < x + 3
y < 2x + 6
So, the second given inequality in slope-intercept form is y < 2x + 6.