Question

3x + 4y = 8

Answer 1

The equation you've provided, \(3x + 4y = 8\), represents a linear equation in two variables, \(x\) and \(y\). We can express \(y\) in terms of \(x\) or vice versa.

Let's solve for \(y\):

1. Start with the equation:
\[
3x + 4y = 8
\]

2. Isolate \(4y\):
\[
4y = 8 - 3x
\]

3. Divide every term by 4:
\[
y = \frac{8 - 3x}{4}
\]

4. This can be simplified to:
\[
y = 2 - \frac{3}{4}x
\]

Now you have \(y\) expressed in terms of \(x\). Alternatively, if you're looking for points on the line, you could consider various values of \(x\) to find corresponding values of \(y\).

If you want to find the intercepts:

- **x-intercept**: Set \(y = 0\):
\[
3x + 4(0) = 8 \Rightarrow 3x = 8 \Rightarrow x = \frac{8}{3}
\]

- **y-intercept**: Set \(x = 0\):
\[
3(0) + 4y = 8 \Rightarrow 4y = 8 \Rightarrow y = 2
\]

So, the intercepts are \(\left(\frac{8}{3}, 0\right)\) and \((0, 2)\).

If there's something specific you'd like to do with this equation, let me know!