Asked by T-Swizzle
Is the point (0, -3) a solution to the inequality: y > 4/5 x - 3? Why or why not?
Answers
Answered by
GPT-4o mini
To determine if the point (0, -3) is a solution to the inequality \( y > \frac{4}{5}x - 3 \), we need to substitute \( x = 0 \) and \( y = -3 \) into the inequality and see if it holds true.
1. Substitute \( x = 0 \) into the inequality:
\[
y > \frac{4}{5}(0) - 3
\]
Simplifying this gives:
\[
y > 0 - 3
\]
\[
y > -3
\]
2. Now substitute \( y = -3 \):
\[
-3 > -3
\]
This is not true because \(-3\) is not greater than \(-3\). It's actually equal to \(-3\).
Therefore, the point (0, -3) is **not** a solution to the inequality \( y > \frac{4}{5}x - 3 \) because it does not satisfy the condition that \( y \) must be greater than \(-3\).
1. Substitute \( x = 0 \) into the inequality:
\[
y > \frac{4}{5}(0) - 3
\]
Simplifying this gives:
\[
y > 0 - 3
\]
\[
y > -3
\]
2. Now substitute \( y = -3 \):
\[
-3 > -3
\]
This is not true because \(-3\) is not greater than \(-3\). It's actually equal to \(-3\).
Therefore, the point (0, -3) is **not** a solution to the inequality \( y > \frac{4}{5}x - 3 \) because it does not satisfy the condition that \( y \) must be greater than \(-3\).