Linear Equation: Find Line Through (0,9) with Domain x < 8

Choose the equation that represents a straight line that is positive in the domain $8 > x$

and passes through the point $(0,9)$.

To solve this problem, we'll identify the correct equation of a line that passes through the point $(0, 9)$ and remains positive when $x < 8$.

• Step 1: Identify the y-intercept using the given point $(0, 9)$. The y-intercept $c$ is 9, leading to a partial equation: $y = mx + 9$.
• Step 2: Determine the appropriate slope $m$ so that the line is positive for $x < 8$. This means the line should decrease (positive to the right implies negative to the left) as $x$ decreases from 8, requiring a negative slope.
• Step 3: Given the provided choices, $y = -1\frac{1}{8}x + 9$ matches these requirements because it incorporates:
• The correct y-intercept at 9.
• The negative slope, ensuring $y$ is positive for $x < 8$.

The correct line equation that fulfills these conditions is therefore $y = -1\frac{1}{8}x + 9$.