Draw the graph for each equation given below, hence find the co-ordinate of the points when the graph drawn meets the co-ordinate axes:
`(2x+15)/3=y-1`

Answer

To solve the equation \((2x + 15)/3 = y - 1\) graphically and find the coordinates where the graph meets the coordinate axes, we will follow these steps:

### Step 1: Rearranging the Equation
First, we need to rearrange the equation to express \(y\) in terms of \(x\).

\[ \frac{2x + 15}{3} = y - 1 \]

Adding 1 to both sides gives:

\[ y = \frac{2x + 15}{3} + 1 \]

Now, we can simplify this further:

\[ y = \frac{2x + 15 + 3}{3} \]

\[ y = \frac{2x + 18}{3} \]

### Step 2: Finding the y-intercept
To find the y-intercept, we set \(x = 0\):

\[ y = \frac{2(0) + 18}{3} = \frac{18}{3} = 6 \]

So, the y-intercept is at the point \((0, 6)\).

### Step 3: Finding the x-intercept
To find the x-intercept, we set \(y = 0\):

\[ 0 = \frac{2x + 18}{3} \]

Multiplying both sides by 3 gives:

\[ 0 = 2x + 18 \]

Subtracting 18 from both sides:

\[ 2x = -18 \]

Dividing by 2:

\[ x = -9 \]

So, the x-intercept is at the point \((-9, 0)\).

### Step 4: Plotting the Points
Now we have two points to plot on the graph:
- The y-intercept: \((0, 6)\)
- The x-intercept: \((-9, 0)\)

### Step 5: Drawing the Graph
Using the points \((0, 6)\) and \((-9, 0)\), we can draw a straight line that represents the equation \((2x + 15)/3 = y - 1\).

### Summary of Points
- The graph meets the y-axis at \((0, 6)\).
- The graph meets the x-axis at \((-9, 0)\).