Let's solve both problems.

Question 6:

We are given:

• Slope ($m$) = 4
• y-intercept ($(0, -9)$).

The slope-intercept form of a line is: $y = mx + b$ Where $m$ is the slope, and $b$ is the y-intercept.

Substitute $m = 4$ and $b = -9$: $y = 4x - 9$

The correct answer is (a).

Question 7:

We are provided with a table for a linear function. First, find the equation of the line using the given points $(-4, -3)$ and $(1, 15)$.

Step 1: Find the slope ($m$):

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{15 - (-3)}{1 - (-4)} = \frac{15 + 3}{1 + 4} = \frac{18}{5} = 3.6$

Step 2: Find the y-intercept ($b$):

Use the point $(1, 15)$ and the slope ($m = 3.6$) in the equation $y = mx + b$: $15 = 3.6(1) + b$ $15 = 3.6 + b \quad \Rightarrow \quad b = 15 - 3.6 = 11.4$

The equation of the line is: $y = 3.6x + 11.4$

Step 3: Fill in missing values:

• For $x = 9.4$: $y = 3.6(9.4) + 11.4 = 33.84 + 11.4 = 45.24$

Thus, the table is filled as:

Would you like further clarifications or additional examples?

Here are some follow-up questions:

1. How do you identify the slope and y-intercept from a linear equation?
2. How can you verify if a point lies on a given line?
3. What is the difference between slope-intercept and standard forms of a line?
4. How do you convert a linear equation into slope-intercept form?
5. What are the key steps to determine the equation of a line given two points?

Tip: Always verify your calculations by substituting values back into the original equation.