Subjects algebra

Line Slope Aae7D0

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **Problem Statement:** Determine the slope of the red line positioned center-right that crosses the x-axis near -240 and 30, and descends diagonally through y-axis values from approximately 50 down to -50. 2. **Formula for slope:** The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Identify points:** From the description, approximate two points on the line: - Point 1: $(x_1, y_1) = (-240, 0)$ (x-intercept near -240) - Point 2: $(x_2, y_2) = (30, 0)$ (x-intercept near 30) However, since both points have $y=0$, this suggests a horizontal line, which contradicts the description of descending diagonally. Instead, use points from y-axis values: - Point 1: $(0, 50)$ (approximate y-intercept) - Point 2: $(30, -50)$ (approximate point crossing positive x-axis near 30 and y near -50) 4. **Calculate slope:** $$m = \frac{-50 - 50}{30 - 0} = \frac{-100}{30} = -\frac{10}{3}$$ 5. **Interpretation:** The slope is approximately $-\frac{10}{3}$, which is a negative slope indicating the line descends from left to right. 6. **Conclusion:** The slope of the center-right red line is $-\frac{10}{3}$, which is not $-1$ or $-\frac{1}{5}$. **Note:** The second red line at the bottom is not analyzed as per instructions to solve only the first problem.