Question

13x + 9y = –11

Answer 1

The equation you've provided, \(13x + 9y = -11\), is a linear equation in two variables (x and y). You can use this equation to find various things, such as the slope, the y-intercept, or to solve for one variable in terms of the other.

### To rewrite the equation in slope-intercept form (y = mx + b):

1. Isolate \(y\):
\[
9y = -13x - 11
\]
2. Divide by 9:
\[
y = -\frac{13}{9}x - \frac{11}{9}
\]

### This gives:
- **Slope (m)**: \(-\frac{13}{9}\)
- **Y-intercept (b)**: \(-\frac{11}{9}\)

### To find specific solutions:
You can choose a value for \(x\) and solve for \(y\) or vice versa.

1. **For example**, let’s find \(y\) when \(x = 0\):
\[
13(0) + 9y = -11 \implies 9y = -11 \implies y = -\frac{11}{9}
\]
So, the point \((0, -\frac{11}{9})\) is on the line.

2. **Now let’s find \(x\) when \(y = 0\)**:
\[
13x + 9(0) = -11 \implies 13x = -11 \implies x = -\frac{11}{13}
\]
So, the point \((- \frac{11}{13}, 0)\) is also on the line.

### Graphing the Equation:
You can plot the points \((0, -\frac{11}{9})\) and \((- \frac{11}{13}, 0)\) on a coordinate plane and draw a straight line through them to represent the equation \(13x + 9y = -11\).

If you have any further questions about this equation or need help with something else, feel free to ask!