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 $(0,9)$ .

Video Solution

Solution Steps

00:00 Choose functions where the given positive domain fits

00:10 Draw the line according to the data

00:16 Positive and negative domains

00:35 The Y-axis intersection point equals the unknown value B

00:49 Use the line equation

00:54 Substitute a point and solve to find the graph's slope

01:04 Isolate the slope M

01:15 This is the function's slope

01:25 Now substitute appropriate values to find the line equation

01:37 And this is the solution to the question

Step-by-Step Solution

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