Which linear inequality is [tex]3 x+4 y>8[/tex] re-written in slope intercept form?
a. [tex]y>-\frac{3}{4} x+2[/tex]
b. [tex]y>\frac{3}{4} x+2[/tex]
c. [tex]x>-\frac{4}{3} x+\frac{8}{3}[/tex]
d. [tex]x>\frac{4}{3} x+\frac{8}{3}[/tex]
Answer (2)
The linear inequality 8"> 3 x + 4 y > 8 rewritten in slope-intercept form is -\frac{3}{4}x + 2"> y > − 4 3 x + 2 . The correct choice is (a).
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To rewrite the linear inequality 8"> 3 x + 4 y > 8 in slope-intercept form, which is mx + b"> y > m x + b , where m represents the slope and b represents the y-intercept, we need to solve the given inequality for y .
Here's how you can do it step-by-step:
Start with the original inequality: 8"> 3 x + 4 y > 8
Subtract 3 x from both sides to isolate terms involving y on one side: -3x + 8"> 4 y > − 3 x + 8
Divide every term by 4 to solve for y : -\frac{3}{4}x + 2"> y > − 4 3 x + 2
Now, the inequality is in slope-intercept form, where the slope m is − 4 3 and the y-intercept b is 2.
Thus, the answer is option (a): -\frac{3}{4} x + 2"> y > − 4 3 x + 2 .
