What is the slope intercept form of the linear equation 3x + 4y = 8?

1 answer

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:

\[ y = -\frac{3}{4}x + 2 \]