2x-y+1=0

To analyze the equation \(2x - y + 1 = 0\), we can rearrange it into the slope-intercept form \(y = mx + b\), where \(m\) represents the slope and \(b\) represents the y-intercept.

Starting with the original equation: \[ 2x - y + 1 = 0 \]

We can isolate \(y\): \[ -y = -2x - 1 \] \[ y = 2x + 1 \]

From this form, we can see that the slope \(m\) is \(2\) and the y-intercept \(b\) is \(1\).

Key Characteristics of the Line:

• Slope: \(2\)
• Y-intercept: \(1\)
• X-intercept: To find the x-intercept, set \(y = 0\): \[ 0 = 2x + 1 \implies 2x = -1 \implies x = -\frac{1}{2} \]

So, the x-intercept is \(-\frac{1}{2}\).

Graphing:

You can graph this line by plotting the y-intercept at the point \((0, 1)\) and using the slope to find another point. From the y-intercept, move up \(2\) units and right \(1\) unit to reach the point \((1, 3)\). Draw a line through these points to represent the equation.

If you have any specific questions about this equation or need further assistance, feel free to ask!