Draw the graph for each equation given below, hence find the co-ordinate of the points when the graph drawn meets the co-ordinate axes:
`1/3x+1/5y=1`

Answer

To solve the equation \( \frac{1}{3}x + \frac{1}{5}y = 1 \) graphically and find the coordinates where the graph meets the coordinate axes, we can follow these steps:

### Step 1: Find the x-intercept
To find the x-intercept, we set \( y = 0 \) in the equation.

\[ \frac{1}{3}x + \frac{1}{5}(0) = 1 \]

This simplifies to:

\[ \frac{1}{3}x = 1 \]

Now, multiply both sides by 3 to solve for \( x \):

\[ x = 3 \]

So, the x-intercept is at the point \( (3, 0) \).

### Step 2: Find the y-intercept
Next, we find the y-intercept by setting \( x = 0 \) in the equation.

\[ \frac{1}{3}(0) + \frac{1}{5}y = 1 \]

This simplifies to:

\[ \frac{1}{5}y = 1 \]

Now, multiply both sides by 5 to solve for \( y \):

\[ y = 5 \]

So, the y-intercept is at the point \( (0, 5) \).

### Step 3: Plot the points
Now that we have the intercepts, we can plot the points \( (3, 0) \) and \( (0, 5) \) on the graph.

### Step 4: Draw the line
After plotting the points, we can draw a straight line through these two points. This line represents the equation \( \frac{1}{3}x + \frac{1}{5}y = 1 \).

### Summary of Points
- The graph meets the x-axis at \( (3, 0) \).
- The graph meets the y-axis at \( (0, 5) \).