Identify the slope and y intercept. Then, graph the linear equation.

In the linear equation \( y = -\frac{1}{4}x + 2 \):

1. The y-intercept \( b \) is the value of \( y \) when \( x = 0 \). From the equation, we can see that: \[ b = 2 \] So, the y-intercept is \( (0, 2) \).

2. The slope \( m \) is the coefficient of \( x \). In this case, the slope is: \[ m = -\frac{1}{4} \] This means that for every 4 units you move to the right (positive direction on the x-axis), you move down 1 unit (negative direction on the y-axis).

To graph the equation:

1. Plot the y-intercept: Start at the point \( (0, 2) \) on the Cartesian plane.
2. Use the slope: From the point \( (0, 2) \):
   • Move 4 units to the right (to \( x = 4 \)), and then move down 1 unit to get the point \( (4, 1) \). Plot this point.
3. Draw the line: Connect the points \( (0, 2) \) and \( (4, 1) \) with a straight line that extends in both directions.

Summary:

• Y-Intercept (b): \( (0, 2) \)
• Slope (m): \( -\frac{1}{4} \)

You can continue plotting additional points using the slope or by selecting different values of \( x \) to get more points to ensure the line is accurate. But the equation represents a straight line that gradually slopes downwards to the right.