The table in the question shows a linear relationship between $x$ and $y$. The task involves finding the slope, y-intercept, and equation of the line.

Step-by-step Explanation:

1. Find the Slope ($m$):

The formula for slope is: $m = \frac{y_2 - y_1}{x_2 - x_1}$

From the table:

• Using $(x_1, y_1) = (-4, 29)$ and $(x_2, y_2) = (-3, 22)$: $m = \frac{22 - 29}{-3 - (-4)} = \frac{-7}{1} = -7$

The slope is -7 (negative).

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

The equation of a line is: $y = mx + b$ Substitute $m = -7$, and one of the points (e.g., $(-4, 29)$): $29 = -7(-4) + b$ $29 = 28 + b$ $b = 29 - 28 = 1$

The y-intercept is $b = 1$, or the point $(0, 1)$.

3. Write the Equation:

Using $m = -7$ and $b = 1$: $y = -7x + 1$

Final Results:

• The slope is negative: $m = -7$
• The y-intercept is $(0, 1)$
• The equation is: $y = -7x + 1$

Would you like additional details or examples to clarify?
Here are 5 related questions to explore further:

1. How do you interpret a slope in a real-world context?
2. Can you determine the equation using a graph instead of points?
3. What happens to the equation if you change the slope or y-intercept?
4. How would the equation change if the points were flipped?
5. How can you test if a point lies on the line of the equation?

Tip: Always double-check calculations by substituting a point into the derived equation to ensure accuracy!