The graph you uploaded shows a straight line, and it appears to follow a negative slope. Let's analyze the key features of this line:

1. Slope:

• The slope is negative, as the line is decreasing from left to right.
• We can find the slope by picking two points on the line. From observation, two easily identifiable points are approximately at $(-12, 12)$ and $(4, -4)$.
• The slope $m$ is calculated using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the points $(-12, 12)$ and $(4, -4)$: $m = \frac{-4 - 12}{4 - (-12)} = \frac{-16}{16} = -1$

2. Y-intercept:

• The line crosses the y-axis at approximately $(0, 0)$, which means the y-intercept is $b = 0$.

3. Equation of the Line:

• Using the slope-intercept form of the equation of a line $y = mx + b$, with $m = -1$ and $b = 0$, the equation of the line is: $y = -x$

Summary:

• Slope: $-1$
• Y-intercept: $0$
• Equation: $y = -x$

Would you like more details on any of these calculations or explanations?

Related Questions:

1. How do you calculate the slope if the points on the graph are less clear?
2. What does the slope of a line tell you about its direction and steepness?
3. How can we confirm the accuracy of the equation of a line?
4. What happens if the y-intercept changes but the slope remains the same?
5. How do you find the x-intercept of a line?

Tip:

When determining the equation of a line, the slope is key to understanding how quickly the line rises or falls, while the y-intercept tells you where the line crosses the vertical axis.