Question

8x + y = –17

Answer 1

The equation you've provided is a linear equation in two variables, \(x\) and \(y\). It can be rewritten or analyzed in various forms depending on what you need. Here are a few ways to work with it:

1. **Slope-Intercept Form**: To express the equation in the slope-intercept form \(y = mx + b\), solve for \(y\):

\[
y = -8x - 17
\]

This indicates that the slope (\(m\)) is -8 and the y-intercept (\(b\)) is -17.

2. **Standard Form**: Your equation is already in standard form \(Ax + By = C\), where \(A = 8\), \(B = 1\), and \(C = -17\).

3. **Graphing**: To graph the line represented by this equation, you can find two points. For example:
- Let \(x = 0\):
\[
y = -8(0) - 17 = -17 \quad \Rightarrow \quad (0, -17)
\]
- Let \(x = 1\):
\[
y = -8(1) - 17 = -25 \quad \Rightarrow \quad (1, -25)
\]
You can then plot these points on a coordinate plane and draw the line through them.

4. **Finding Intercepts**:
- **y-intercept**: Set \(x = 0\):
\[
y = -17 \quad \Rightarrow \quad (0, -17)
\]
- **x-intercept**: Set \(y = 0\):
\[
0 = -8x - 17 \quad \Rightarrow \quad 8x = -17 \quad \Rightarrow \quad x = -\frac{17}{8} = -2.125 \quad \Rightarrow \quad \left(-\frac{17}{8}, 0\right)
\]

If you need further analysis or a specific type of solution related to this equation, please let me know!