To determine the slope and the y-intercept from the table of values, we'll first find the slope $m$, using the formula for the slope between two points:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Let’s use the points $(0, 6)$ and $(1, 4)$:

$m = \frac{4 - 6}{1 - 0} = \frac{-2}{1} = -2$

So, the slope $m = -2$.

Now, to find the y-intercept, we can use the slope-intercept form of a line $y = mx + b$. Since we know the slope $m = -2$, we can substitute one of the points from the table (for example, $(0, 6)$) into the equation to find the y-intercept $b$.

At $x = 0$, $y = 6$:

$y = mx + b \implies 6 = -2(0) + b \implies b = 6$

Thus, the y-intercept is $b = 6$.

Final Answer:

• Slope = $-2$
• Y-intercept = $6$

Would you like further details or have any questions?

Here are some related questions to explore:

1. How do you calculate the slope if given other pairs of points?
2. What is the equation of the line based on this slope and y-intercept?
3. How does the slope affect the steepness of the line?
4. What happens to the y-intercept if the entire line shifts up or down?
5. How can you use this information to graph the line?

Tip: The y-intercept is always the value of $y$ when $x = 0$.