Write the coordinates of the point where the graph of the equation 5x+2y =10 intersect both the axes

Answer

To find the coordinates of the points where the graph of the equation \(5x + 2y = 10\) intersects both the x-axis and the y-axis, we will calculate the x-intercept and the y-intercept.

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

\[ 5x + 2(0) = 10 \]

This simplifies to:

\[ 5x = 10 \]

Now, divide both sides by 5:

\[ x = \frac{10}{5} = 2 \]

Thus, the x-intercept is at the point \((2, 0)\).

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

\[ 5(0) + 2y = 10 \]

This simplifies to:

\[ 2y = 10 \]

Now, divide both sides by 2:

\[ y = \frac{10}{2} = 5 \]

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

### Final Answer
The coordinates of the points where the graph intersects the axes are:
- x-intercept: \((2, 0)\)
- y-intercept: \((0, 5)\)