This graph shows a straight line with a negative slope, indicating that as $x$ increases, $y$ decreases. Let's determine the slope and the equation of the line.

1. Slope Calculation

To find the slope $m$, we can use two points the line passes through. From the graph, the line passes through:

• Point $(-4, 4)$
• Point $(4, -2)$

The formula for slope is:

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

Substituting the points $(-4, 4)$ and $(4, -2)$:

$m = \frac{-2 - 4}{4 - (-4)} = \frac{-6}{8} = -\frac{3}{4}$

2. Equation of the Line

The slope-intercept form of a line is:

$y = mx + b$

Using the slope $m = -\frac{3}{4}$ and one point, let's substitute point $(4, -2)$ into the equation to find $b$ (the y-intercept):

$-2 = -\frac{3}{4}(4) + b$

Simplifying:

$-2 = -3 + b$ $b = 1$

Thus, the equation of the line is:

$y = -\frac{3}{4}x + 1$

Summary:

• Slope: $-\frac{3}{4}$
• Equation of the line: $y = -\frac{3}{4}x + 1$

Would you like further details or explanations?

Here are some related questions:

1. How would the line change if the slope was positive instead of negative?
2. What is the significance of the y-intercept in the equation of a line?
3. How would you convert this equation into standard form $Ax + By = C$?
4. What is the relationship between parallel lines and their slopes?
5. How does the steepness of a line relate to the absolute value of its slope?

Tip: When interpreting a graph, remember that negative slopes always indicate that the line falls as $x$ increases!