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 convert the given system of inequalities into slope-intercept form (\(y = mx + b\)), we will rearrange both inequalities.

1. **For the first inequality:**
\[
4x - 5y < 1
\]
First, isolate \(y\):
\[
-5y < 1 - 4x
\]
Divide by -5 (remembering to flip the inequality sign):
\[
y > \frac{4}{5}x - \frac{1}{5}
\]

2. **For the second inequality:**
\[
\frac{1}{2}y - x < 3
\]
First, isolate \(y\):
\[
\frac{1}{2}y < 3 + x
\]
Multiply through by 2:
\[
y < 2x + 6
\]

So, the inequalities in slope-intercept form are:

1. \(y > \frac{4}{5}x - \frac{1}{5}\) (from the first inequality)
2. \(y < 2x + 6\) (from the second inequality)

From the options provided, the correct representation of the inequalities in slope-intercept form is:

- \(y > \frac{4}{5}x - \frac{1}{5}\)
- \(y < 2x + 6\)

Therefore, the choices relevant to these results in the system of inequalities would be \(y > \frac{4}{5}x - \frac{1}{5}\) and \(y < 2x + 6\).