To solve this, we will calculate the slope and y-intercept of the linear function given the table of values.

Step 1: Find the slope (m)

The formula for the slope $m$ of a linear function is: $m = \frac{{y_2 - y_1}}{{x_2 - x_1}}$ We can pick any two points from the table to find the slope. Let's use the points $(0, -2)$ and $(3, -4)$.

$m = \frac{{-4 - (-2)}}{{3 - 0}} = \frac{{-4 + 2}}{{3}} = \frac{{-2}}{{3}}$ So, the slope is $m = -\frac{2}{3}$.

Step 2: Find the y-intercept (b)

The y-intercept is the value of $y$ when $x = 0$. From the table, when $x = 0$, $y = -2$. Thus, the y-intercept is $b = -2$.

Final Answer:

• Slope: $-\frac{2}{3}$
• y-intercept: $-2$

Would you like more details or have any questions?

Here are 5 related questions to expand on this:

1. How do you interpret the slope of a linear function geometrically?
2. What happens to the graph if the slope is positive instead of negative?
3. Can you use other pairs of points from the table to confirm the slope is the same?
4. How does the y-intercept help in graphing the line quickly?
5. What would be the equation of this line in slope-intercept form?

Tip: Always use the slope formula consistently, but remember that for a linear equation, the slope between any two points on the line should be the same.