Draw the graph for the lienar equation
3x+4y=12 if x =8 find the value of y with the help of graph

Answer

To solve the problem step by step, we will first graph the linear equation \(3x + 4y = 12\) and then find the value of \(y\) when \(x = 8\).

### Step 1: Write the equation
The given linear equation is:
\[ 3x + 4y = 12 \]

### Step 2: Find points to plot the graph
To graph the equation, we need at least two points. We can find these points by substituting values for \(x\) and \(y\).

#### Finding the y-intercept (when \(x = 0\)):
Substituting \(x = 0\):
\[ 3(0) + 4y = 12 \implies 4y = 12 \implies y = \frac{12}{4} = 3 \]
So, one point is \((0, 3)\).

#### Finding the x-intercept (when \(y = 0\)):
Substituting \(y = 0\):
\[ 3x + 4(0) = 12 \implies 3x = 12 \implies x = \frac{12}{3} = 4 \]
So, another point is \((4, 0)\).

### Step 3: Plot the points on the graph
Now we have two points:
1. \((0, 3)\)
2. \((4, 0)\)

We can plot these points on a Cartesian plane.

### Step 4: Draw the line
Once the points are plotted, we can draw a straight line through these two points. This line represents the equation \(3x + 4y = 12\).

### Step 5: Find the value of \(y\) when \(x = 8\)
To find \(y\) when \(x = 8\), we can extend the line we drew. We can also substitute \(x = 8\) into the original equation to find \(y\):
\[ 3(8) + 4y = 12 \implies 24 + 4y = 12 \implies 4y = 12 - 24 \implies 4y = -12 \implies y = \frac{-12}{4} = -3 \]
Thus, when \(x = 8\), \(y = -3\).

### Final Answer
The value of \(y\) when \(x = 8\) is:
\[ y = -3 \]