Find the slope and y-intercept of the line : 
` ax - by = 0`

Answer

To find the slope and y-intercept of the line given by the equation \( ax - by = 0 \), we will follow these steps:

### Step 1: Rewrite the equation in slope-intercept form
The slope-intercept form of a line is given by the equation:
\[ y = mx + c \]
where \( m \) is the slope and \( c \) is the y-intercept. We need to rearrange the given equation \( ax - by = 0 \) into this form.

### Step 2: Solve for \( y \)
Starting from the equation:
\[ ax - by = 0 \]
we can isolate \( y \) by moving \( ax \) to the other side:
\[ -by = -ax \]
Now, divide both sides by \(-b\) (assuming \( b \neq 0 \)):
\[ y = \frac{a}{b}x + 0 \]

### Step 3: Identify the slope and y-intercept
From the equation \( y = \frac{a}{b}x + 0 \), we can see that:
- The slope \( m \) is \( \frac{a}{b} \).
- The y-intercept \( c \) is \( 0 \).

### Conclusion
Thus, the slope of the line is \( \frac{a}{b} \) and the y-intercept is \( 0 \). This indicates that the line passes through the origin.

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