Question

5x − 6y = 8

Answer 1

The equation you provided, \(5x - 6y = 8\), is a linear equation in two variables (x and y). To express this equation in a more useful form, such as the slope-intercept form \(y = mx + b\), we can solve for \(y\).

Here’s how you can do it:

1. Start with the original equation:
\[
5x - 6y = 8
\]

2. Subtract \(5x\) from both sides:
\[
-6y = -5x + 8
\]

3. Divide every term by \(-6\):
\[
y = \frac{5}{6}x - \frac{8}{6}
\]

4. Simplify \(-\frac{8}{6}\) to \(-\frac{4}{3}\):
\[
y = \frac{5}{6}x - \frac{4}{3}
\]

Now, the equation is in slope-intercept form, where the slope \(m = \frac{5}{6}\) and the y-intercept \(b = -\frac{4}{3}\).

If you want to find specific values of \(x\) and \(y\) that satisfy the equation or graph it, please provide additional details!