Subjects algebra

Line Equations 318C14

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1. The problem involves finding the equations of two lines, C and D, given their intercepts. 2. The formula for the equation of a line using intercepts is $$y = m x + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. For line C: - Y-intercept $b = 10$ (crosses y-axis at (0,10)) - X-intercept is approximately $(3.5, 0)$ - Slope $m = \frac{0 - 10}{3.5 - 0} = \frac{-10}{3.5} = -\frac{20}{7}$ 4. Equation of line C: $$y = -\frac{20}{7} x + 10$$ 5. For line D: - Y-intercept $b = -4$ (crosses y-axis at (0,-4)) - X-intercept is approximately $(6, 0)$ - Slope $m = \frac{0 - (-4)}{6 - 0} = \frac{4}{6} = \frac{2}{3}$ 6. Equation of line D: $$y = \frac{2}{3} x - 4$$ 7. These equations describe the lines C and D based on the given intercepts.