1. **State the problem:** We have two lines graphed on a coordinate plane and need to find their equations and estimate the solution to the system formed by these lines. 2. **Identify points on each line:** - Line 1 passes through approximately (0,10), (5,5), and (10,0). - Line 2 passes through approximately (0,20) and (10,0). 3. **Find the slope of each line using the formula** $m=\frac{y_2 - y_1}{x_2 - x_1}$. For Line 1: $$m_1 = \frac{5 - 10}{5 - 0} = \frac{-5}{5} = -1$$ For Line 2: $$m_2 = \frac{0 - 20}{10 - 0} = \frac{-20}{10} = -2$$ 4. **Write the equation of each line in slope-intercept form** $y = mx + b$. For Line 1, using point (0,10): $$y = -1 \cdot x + b$$ Substitute $x=0$, $y=10$: $$10 = -1 \cdot 0 + b \Rightarrow b = 10$$ Equation 1: $$y = -x + 10$$ For Line 2, using point (0,20): $$y = -2x + b$$ Substitute $x=0$, $y=20$: $$20 = -2 \cdot 0 + b \Rightarrow b = 20$$ Equation 2: $$y = -2x + 20$$ 5. **Estimate the solution to the system by finding the intersection point:** Set the two equations equal: $$-x + 10 = -2x + 20$$ Add $2x$ to both sides: $$-x + 2x + 10 = 20$$ $$x + 10 = 20$$ Subtract 10 from both sides: $$x = 10$$ Substitute $x=10$ into Equation 1: $$y = -10 + 10 = 0$$ 6. **Final answer:** - Equation 1: $y = -x + 10$ - Equation 2: $y = -2x + 20$ - Solution to the system: $(10, 0)$