Question

9y=x+4
Find the x and y intercept of the line

Answer 1

To find the x-intercept and y-intercept of the equation \(9y = x + 4\), we can rearrange the equation into slope-intercept form (y = mx + b) first:

1. Rearrange to get \(y\) by itself:
\[
9y = x + 4
\]
\[
y = \frac{1}{9}x + \frac{4}{9}
\]

### Finding the y-intercept:
The y-intercept occurs where \(x = 0\).
Substituting \(x = 0\) into the equation:
\[
y = \frac{1}{9}(0) + \frac{4}{9} = \frac{4}{9}
\]
So, the y-intercept is \( \left(0, \frac{4}{9}\right) \).

### Finding the x-intercept:
The x-intercept occurs where \(y = 0\).
Substituting \(y = 0\) into the original equation:
\[
9(0) = x + 4
\]
\[
0 = x + 4
\]
\[
x = -4
\]
So, the x-intercept is \( (-4, 0) \).

### Summary:
- y-intercept: \( \left(0, \frac{4}{9}\right) \)
- x-intercept: \( (-4, 0) \)