Draw the graph for ` (2x-1)/3 - (y-2)/5=0` Also find the co ordinates of the points where the graph line) drawn meets the co-ordinate axes.

Answer

To solve the equation \( \frac{2x - 1}{3} - \frac{y - 2}{5} = 0 \) and find the points where the line meets the coordinate axes, we can follow these steps:

### Step 1: Rearranging the Equation
Start by rearranging the given equation to a more standard form.

\[ \frac{2x - 1}{3} = \frac{y - 2}{5} \]

Cross-multiplying gives:

\[ 5(2x - 1) = 3(y - 2) \]

### Step 2: Expand and Simplify
Expanding both sides:

\[ 10x - 5 = 3y - 6 \]

Now, rearranging this to isolate \(y\):

\[ 3y = 10x - 5 + 6 \]
\[ 3y = 10x + 1 \]
\[ y = \frac{10}{3}x + \frac{1}{3} \]

### Step 3: Finding Intercepts
To find where the line meets the x-axis and y-axis, we can set \(y = 0\) for the x-intercept and \(x = 0\) for the y-intercept.

#### Finding the x-intercept:
Set \(y = 0\):

\[ 0 = \frac{10}{3}x + \frac{1}{3} \]

Solving for \(x\):

\[ \frac{10}{3}x = -\frac{1}{3} \]
\[ 10x = -1 \]
\[ x = -\frac{1}{10} \]

So, the x-intercept is \((- \frac{1}{10}, 0)\).

#### Finding the y-intercept:
Set \(x = 0\):

\[ y = \frac{10}{3}(0) + \frac{1}{3} \]
\[ y = \frac{1}{3} \]

So, the y-intercept is \((0, \frac{1}{3})\).

### Step 4: Plotting the Points and Drawing the Graph
Now that we have the intercepts, we can plot the points:

1. Point A: \((0, \frac{1}{3})\)
2. Point B: \((- \frac{1}{10}, 0)\)

Draw the x-axis and y-axis, then plot these points. Finally, draw a straight line through these two points.

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