Question

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

y=−
1
4​x+2



Begin with
b,the y-intercept:

Move with
m,the slope:

Answer 1

To identify the slope and y-intercept from the equation \( y = -\frac{1}{4}x + 2 \), we can follow these steps:

### Step 1: Identify the y-intercept
In the slope-intercept form of the equation \( y = mx + b \):
- \( m \) is the slope
- \( b \) is the y-intercept

From the equation:
- The y-intercept \( b = 2 \).
This means the graph crosses the y-axis at the point (0, 2).

### Step 2: Identify the slope
The slope \( m \) from the equation is:
- \( m = -\frac{1}{4} \).
This indicates that for every 4 units you move to the right (positive x-direction), you move 1 unit down (negative y-direction).

### Step 3: Graph the linear equation
1. **Plot the y-intercept**:
- Start at the point (0, 2).

2. **Use the slope to find another point**:
- From (0, 2), move 4 units to the right (to x = 4) and 1 unit down (to y = 1). This gives you the point (4, 1).
- You can also move in the opposite direction by going 4 units to the left (to x = -4) and 1 unit up (to y = 3), giving you the point (-4, 3).

3. **Draw the line**:
- Connect the points (0, 2) and (4, 1) with a straight line. Extend this line in both directions.

Now, you should have a graph of the line represented by the equation \( y = -\frac{1}{4}x + 2 \). The line slopes downward from left to right due to the negative slope.