13x + 9y = –11

1 answer

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!