Question

7X minus 3Y equals -21

Answer 1

The equation you've provided is in the linear form \(7X - 3Y = -21\).

To analyze or manipulate this equation, we can express it in different forms. Here are a few common forms:

1. **Slope-Intercept Form**: This form is expressed as \(Y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
- Start by isolating \(Y\):
\[
-3Y = -7X - 21
\]
\[
Y = \frac{7}{3}X + 7
\]
So, the slope \(m\) is \(\frac{7}{3}\) and the y-intercept \(b\) is 7.

2. **Standard Form**: The equation is already in standard form \(Ax + By = C\) where \(A = 7\), \(B = -3\), and \(C = -21\).

3. **Finding Intercepts**:
- **X-intercept**: Set \(Y = 0\):
\[
7X - 3(0) = -21 \Rightarrow 7X = -21 \Rightarrow X = -3
\]
So the x-intercept is \((-3, 0)\).

- **Y-intercept**: Set \(X = 0\):
\[
7(0) - 3Y = -21 \Rightarrow -3Y = -21 \Rightarrow Y = 7
\]
So the y-intercept is \((0, 7)\).

If you need further calculations, graphing, or solutions for specific values for \(X\) or \(Y\), let me know!