To convert the linear equation \(3x + 4y = 8\) into slope-intercept form, which is \(y = mx + b\) (where \(m\) is the slope and \(b\) is the y-intercept), we need to solve for \(y\).
Starting with the original equation:
\[ 3x + 4y = 8 \]
Subtract \(3x\) from both sides:
\[ 4y = -3x + 8 \]
Next, divide every term by \(4\):
\[ y = -\frac{3}{4}x + 2 \]
Now, the equation is in slope-intercept form \(y = mx + b\), where \(m = -\frac{3}{4}\) (the slope) and \(b = 2\) (the y-intercept).
Thus, the slope-intercept form of the equation \(3x + 4y = 8\) is:
\[ y = -\frac{3}{4}x + 2 \]