Draw the graph of straight line ` y = - 2x + 3 ` use your graph of find :
the intercept on y-axis

Answer

To draw the graph of the straight line given by the equation \( y = -2x + 3 \) and find the intercept on the y-axis, we can follow these steps:

### Step 1: Identify the y-intercept
The y-intercept can be found by setting \( x = 0 \) in the equation.

\[ y = -2(0) + 3 = 3 \]

So, the y-intercept is \( (0, 3) \).

### Step 2: Identify the x-intercept
To find the x-intercept, we set \( y = 0 \) in the equation.

\[ 0 = -2x + 3 \]

Rearranging gives:

\[ 2x = 3 \implies x = \frac{3}{2} \]

So, the x-intercept is \( \left(\frac{3}{2}, 0\right) \).

### Step 3: Plot the intercepts on the graph
Now, we can plot the points we found:
- The y-intercept \( (0, 3) \) on the y-axis.
- The x-intercept \( \left(\frac{3}{2}, 0\right) \) on the x-axis.

### Step 4: Draw the line
Using a ruler, draw a straight line through the two points plotted. This line represents the equation \( y = -2x + 3 \).

### Step 5: Identify the y-intercept from the graph
From the graph, we can see that the intercept on the y-axis is the point where the line crosses the y-axis, which we calculated as \( (0, 3) \).

### Final Answer
The intercept on the y-axis is \( 3 \).

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