Question

Given the system of inequalities:

4x – 5y < 1

One-halfy – x < 3





Which shows the given inequalities in slope-intercept form?


y < Four-fifthsx – One-fifth

y < 2x + 6

y > Four-fifthsx – One-fifths

y < 2x + 6

y > Negative four-fifthsx + One-fifth

y > 2x + 6

Answer 1

To write the given system of inequalities in slope-intercept form, solve each inequality for y. The system of inequalities in slope-intercept form is: y > (4/5)x - 1/5 and y < 2x + 6.

Step-by-step explanation:

To write the given system of inequalities in slope-intercept form, we need to solve each inequality for y.

Starting with the first inequality, 4x – 5y < 1:

1. Subtract 4x from both sides: -5y < -4x + 1
2. Divide both sides by -5. Since we are dividing by a negative number, the inequality sign flips: y > (4/5)x - 1/5

Now, let's solve the second inequality, One-halfy – x < 3:

1. Add x to both sides: One-halfy < x + 3
2. Double both sides to eliminate the fraction: y < 2x + 6

Therefore, the system of inequalities in slope-intercept form is: y > (4/5)x - 1/5 and y < 2x + 6.

Answer 2

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: