Subjects algebra

Line Segment

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Line Segment


1. The problem presents a coordinate plane with x and y axes labeled from -7 to 7, and a line segment plotted roughly along $y = x$ from $(-5, -6)$ to $(5, 6)$. 2. We are asked to analyze the line and verify its equation or characteristics. 3. First, check the slope $m$ using the endpoints: $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - (-6)}{5 - (-5)} = \frac{12}{10} = 1.2.$$ 4. The slope is approximately $1.2$, close to 1 but slightly different. 5. Next, find the equation of the line in the form $y = mx + b$. Use one point, for example $(-5, -6)$: $$-6 = 1.2 \times (-5) + b \Rightarrow -6 = -6 + b \Rightarrow b = 0.$$ 6. So, the line equation is approximately: $$y = 1.2x.$$ 7. The line is similar to $y = x$ but slightly steeper, confirmed by the slope and position of endpoints. 8. Therefore, the plotted line segment extends roughly from $(-5, -6)$ to $(5, 6)$ with equation $y = 1.2x$.