Draw the graph for each equation given below:
`(2x-1)/3-(y-2)/5=0`
In each case find the co-ordinate of the points where the graph (line) drawn meets the co-ordinate axes.

Answer

To solve the equation `(2x-1)/3 - (y-2)/5 = 0` and find the points where the graph meets the coordinate axes, we will follow these steps:

### Step 1: Rearranging the Equation
Start with the given equation:
\[ \frac{2x - 1}{3} - \frac{y - 2}{5} = 0 \]
To eliminate the fractions, we can multiply through by the least common multiple of the denominators, which is 15:
\[ 15 \left( \frac{2x - 1}{3} \right) - 15 \left( \frac{y - 2}{5} \right) = 0 \]
This simplifies to:
\[ 5(2x - 1) - 3(y - 2) = 0 \]
Expanding this gives:
\[ 10x - 5 - 3y + 6 = 0 \]
Combining like terms results in:
\[ 10x - 3y + 1 = 0 \]

### Step 2: Finding Intercepts
To find where the line meets the coordinate axes, we will calculate the x-intercept and y-intercept.

#### Finding the y-intercept
Set \(x = 0\) in the equation:
\[ 10(0) - 3y + 1 = 0 \]
This simplifies to:
\[ -3y + 1 = 0 \implies 3y = 1 \implies y = \frac{1}{3} \]
Thus, the y-intercept is at the point \((0, \frac{1}{3})\).

#### Finding the x-intercept
Set \(y = 0\) in the equation:
\[ 10x - 3(0) + 1 = 0 \]
This simplifies to:
\[ 10x + 1 = 0 \implies 10x = -1 \implies x = -\frac{1}{10} \]
Thus, the x-intercept is at the point \((- \frac{1}{10}, 0)\).

### Step 3: Plotting the Points and Drawing the Graph
Now we have two points:
1. \( (0, \frac{1}{3}) \)
2. \( (-\frac{1}{10}, 0) \)

Plot these points on the Cartesian plane:
- The point \( (0, \frac{1}{3}) \) is on the y-axis.
- The point \( (-\frac{1}{10}, 0) \) is on the x-axis.

Draw a straight line through these two points to represent the graph of the equation.

### Conclusion
The coordinates of the points where the graph meets the coordinate axes are:
- Y-intercept: \( (0, \frac{1}{3}) \)
- X-intercept: \( (-\frac{1}{10}, 0) \)