Draw the graph for each equation given below:
`2x-5y=10`
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 \(2x - 5y = 10\) and draw its graph, we will follow these steps:

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

\[ 2x - 5(0) = 10 \]
\[ 2x = 10 \]
\[ x = \frac{10}{2} = 5 \]

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

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

\[ 2(0) - 5y = 10 \]
\[ -5y = 10 \]
\[ y = \frac{10}{-5} = -2 \]

So, the y-intercept is at the point \((0, -2)\).

### Step 3: Plot the points
Now we have two points:
1. The x-intercept: \((5, 0)\)
2. The y-intercept: \((0, -2)\)

We will plot these points on the Cartesian plane.

### Step 4: Draw the graph
After plotting the points \((5, 0)\) and \((0, -2)\), we will draw a straight line through these points. This line represents the equation \(2x - 5y = 10\).

### Final Answer
The graph of the equation \(2x - 5y = 10\) is a straight line that intersects the x-axis at \((5, 0)\) and the y-axis at \((0, -2)\).

---