Draw the graph of equation `x/4+y/5=1`. Use the graph drawn to find:
(i) `x_(1)` the value of x, when y=10
(ii) `y_(1)` the value of y, when x=8

Answer

To solve the equation \( \frac{x}{4} + \frac{y}{5} = 1 \) and find the required values, we will follow these steps:

### Step 1: Rearranging the Equation
We start by rearranging the equation to solve for \( y \):
\[ \frac{y}{5} = 1 - \frac{x}{4} \]
Multiplying both sides by 5 gives:
\[ y = -\frac{5}{4}x + 5 \]

### Step 2: Finding Points to Plot the Graph
We will find some points by substituting values for \( x \) into the equation \( y = -\frac{5}{4}x + 5 \).

- For \( x = 0 \):
\[ y = -\frac{5}{4}(0) + 5 = 5 \quad \Rightarrow \quad (0, 5) \]

- For \( x = 4 \):
\[ y = -\frac{5}{4}(4) + 5 = -5 + 5 = 0 \quad \Rightarrow \quad (4, 0) \]

- For \( x = 8 \):
\[ y = -\frac{5}{4}(8) + 5 = -10 + 5 = -5 \quad \Rightarrow \quad (8, -5) \]

### Step 3: Plotting the Points
Now we plot the points \( (0, 5) \), \( (4, 0) \), and \( (8, -5) \) on a graph and draw a straight line through these points.

### Step 4: Finding \( x_1 \) when \( y = 10 \)
Substituting \( y = 10 \) into the original equation:
\[ \frac{x}{4} + \frac{10}{5} = 1 \]
This simplifies to:
\[ \frac{x}{4} + 2 = 1 \]
Subtracting 2 from both sides:
\[ \frac{x}{4} = 1 - 2 = -1 \]
Multiplying both sides by 4 gives:
\[ x = -4 \]
Thus, \( x_1 = -4 \).

### Step 5: Finding \( y_1 \) when \( x = 8 \)
Substituting \( x = 8 \) into the rearranged equation:
\[ y = -\frac{5}{4}(8) + 5 \]
Calculating this gives:
\[ y = -10 + 5 = -5 \]
Thus, \( y_1 = -5 \).

### Final Answer
The values are:
- \( x_1 = -4 \) when \( y = 10 \)
- \( y_1 = -5 \) when \( x = 8 \)