writing linear eqautions from standard form to slope-intercept form

Question

8x+2y=10

Answer 1

To convert the equation \(8x + 2y = 10\) from standard form to slope-intercept form (which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept), follow these steps:

1. Start with the standard form of the equation:

   \[ 8x + 2y = 10 \]

2. Isolate \(y\) by moving the \(8x\) term to the right side of the equation:

   \[ 2y = -8x + 10 \]

3. Divide every term by 2 to solve for \(y\):

   \[ y = -4x + 5 \]

Now the equation is in slope-intercept form, where the slope \(m\) is \(-4\) and the y-intercept \(b\) is \(5\).

So, the final answer is:

\[ y = -4x + 5 \]