(i)sketch the graph y=4-x and `y= log_(10)x` on same graph .
(ii) write down the equation to find the x-coordinate of the point of intersection of graphs

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the Functions
We have two functions to graph:
1. \( y = 4 - x \) (a linear function)
2. \( y = \log_{10} x \) (a logarithmic function)

### Step 2: Create a Table of Values for the Linear Function
For the linear function \( y = 4 - x \), we can create a table of values:

| \( x \) | \( y = 4 - x \) |
|---------|------------------|
| 0 | 4 |
| 4 | 0 |

### Step 3: Plot the Linear Function
Using the points from the table:
- Plot the point (0, 4) on the graph.
- Plot the point (4, 0) on the graph.
- Draw a straight line through these points.

### Step 4: Create a Table of Values for the Logarithmic Function
For the logarithmic function \( y = \log_{10} x \), we can create a table of values:

| \( x \) | \( y = \log_{10} x \) |
|---------|------------------------|
| 1 | 0 |
| 10 | 1 |
| 100 | 2 |

### Step 5: Plot the Logarithmic Function
Using the points from the table:
- Plot the point (1, 0) on the graph.
- Plot the point (10, 1) on the graph.
- Plot the point (100, 2) on the graph.
- Draw the curve of the logarithmic function, which approaches the y-axis but never touches it.

### Step 6: Identify the Point of Intersection
To find the x-coordinate of the point where the two graphs intersect, we set the two equations equal to each other:
\[ 4 - x = \log_{10} x \]

### Step 7: Write Down the Equation
The equation to find the x-coordinate of the point of intersection is:
\[ 4 - x = \log_{10} x \]

### Summary
We have sketched the graphs of \( y = 4 - x \) and \( y = \log_{10} x \) and found the equation to determine the x-coordinate of their intersection.

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