Q:

Given the system of inequalities: 4x – 5y < 1y – x < 3Which shows the given inequalities in slope-intercept form?the answer is B y > x – y < 2x + 6the answer is B

Accepted Solution

A:
Answer:
First inequality: y > [tex] \frac{4}{5} x - \frac{1}{5} [/tex]
Second inequality: y < 3 + x

Explanation:
The inequality in slope-intercept form has the following general formula:
y < mx + c or y > mx + c (according to the given sign)
where m is the slope and c is the y-intercept

This means that to get any inequality in slope-intercept form, we will have to isolate the y on one side of the inequality.

First given inequality:
4x - 5y < 1
4x - 5y + 5y < 1 + 5y
1 + 5y > 4x
1 + 5y - 1 > 4x - 1
5y > 4x - 1
y > [tex] \frac{4}{5} x - \frac{1}{5} [/tex]
comparing this to the general form, we would find that:
slope (m) = 4/5
y-intercept (c) = 1/5

Second given inequality:
y - x < 3
y - x + x < 3 + x
y < 3 + x
comparing this to the general form, we would find that:
slope (m) = 1
y-intercept (c) = 3

Hope this helps :)