convert the following equations from. standard form to slope-intercept form

Question

x+2y=4

Answer 1

To convert the equation \( x + 2y = 4 \) 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 original equation: \[ x + 2y = 4 \]

2. Isolate the \( y \)-term by subtracting \( x \) from both sides: \[ 2y = -x + 4 \]

3. Divide every term by 2 to solve for \( y \): \[ y = -\frac{1}{2}x + 2 \]

Now the equation is in slope-intercept form.

Thus, the final result is: \[ y = -\frac{1}{2}x + 2 \]

Here, the slope \( m = -\frac{1}{2} \) and the y-intercept \( b = 2 \).