Draw the graph of `y=2x-1`

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Answer

To draw the graph of the equation \( y = 2x - 1 \), we can follow these steps:

### Step 1: Identify the equation
The given equation is \( y = 2x - 1 \). This is in the slope-intercept form \( y = mx + c \), where \( m \) is the slope and \( c \) is the y-intercept.

### Step 2: Determine the slope and y-intercept
From the equation \( y = 2x - 1 \):
- The slope \( m = 2 \)
- The y-intercept \( c = -1 \)

This means the line crosses the y-axis at the point \( (0, -1) \).

### Step 3: Plot the y-intercept
On the graph, locate the y-axis and mark the point \( (0, -1) \).

### Step 4: Find another point by setting \( x = 0 \)
Next, we can find another point by setting \( x = 0 \):
- When \( x = 0 \):
\[ y = 2(0) - 1 = -1 \]
So, we have the point \( (0, -1) \).

### Step 5: Find another point by setting \( y = 0 \)
Now, let's find another point by setting \( y = 0 \):
- Set \( y = 0 \):
\[ 0 = 2x - 1 \]
\[ 2x = 1 \quad \Rightarrow \quad x = \frac{1}{2} \]
So, we have the point \( \left(\frac{1}{2}, 0\right) \).

### Step 6: Plot the second point
On the graph, locate the point \( \left(\frac{1}{2}, 0\right) \).

### Step 7: Draw the line
Now that we have two points, \( (0, -1) \) and \( \left(\frac{1}{2}, 0\right) \), we can draw a straight line through these points. This line represents the graph of the equation \( y = 2x - 1 \).

### Final Graph
The graph will be a straight line that rises steeply due to the slope of 2, crossing the y-axis at -1 and the x-axis at \( \frac{1}{2} \).

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