A line is represented by the equation `y=zx+18`. If this line intersects the x - axis at `(-3, 0)`, what is z?

Answer

To find the value of \( z \) in the equation of the line \( y = zx + 18 \) that intersects the x-axis at the point \((-3, 0)\), we can follow these steps:

### Step 1: Understand the given information
We know that the equation of the line is given by:
\[ y = zx + 18 \]
The line intersects the x-axis at the point \((-3, 0)\). This means that when \( x = -3 \), \( y \) must be \( 0 \).

### Step 2: Substitute the point into the equation
Since the line passes through the point \((-3, 0)\), we can substitute \( x = -3 \) and \( y = 0 \) into the equation:
\[ 0 = z(-3) + 18 \]

### Step 3: Simplify the equation
Now, simplify the equation:
\[ 0 = -3z + 18 \]

### Step 4: Solve for \( z \)
To isolate \( z \), we can rearrange the equation:
\[ 3z = 18 \]
Now, divide both sides by \( 3 \):
\[ z = \frac{18}{3} = 6 \]

### Conclusion
Thus, the value of \( z \) is:
\[ \boxed{6} \]

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