Question

Find the x- and y-intercepts of the line y=–9x–9/8
.

Answer 1

To find the x- and y-intercepts of the line given by the equation \( y = -9x - \frac{9}{8} \), we will follow these steps:

**1. Finding the y-intercept:**
The y-intercept occurs when \( x = 0 \).

Substituting \( x = 0 \) into the equation:
\[
y = -9(0) - \frac{9}{8} = -\frac{9}{8}
\]

So, the y-intercept is:
\[
(0, -\frac{9}{8})
\]

**2. Finding the x-intercept:**
The x-intercept occurs when \( y = 0 \).

Setting \( y = 0 \) and substituting into the equation:
\[
0 = -9x - \frac{9}{8}
\]

Now, solve for \( x \):
\[
9x = -\frac{9}{8}
\]
\[
x = -\frac{9}{8 \cdot 9} = -\frac{1}{8}
\]

So, the x-intercept is:
\[
(-\frac{1}{8}, 0)
\]

**Summary of intercepts:**
- y-intercept: \( (0, -\frac{9}{8}) \)
- x-intercept: \( (-\frac{1}{8}, 0) \)