Linear Equations 5Fb6Fa

1. The problem is to understand how to solve linear equations and find intercepts step by step. 2. The standard form of a linear equation is $$Ax + By = C$$. 3. To find the y-intercept, set $$x = 0$$ and solve for $$y$$. 4. To find the x-intercept, set $$y = 0$$ and solve for $$x$$. 5. Example: For the equation $$2x + 3y = 12$$, - Find y-intercept: Set $$x=0$$, then $$3y = 12$$, so $$y = \frac{12}{3} = 4$$. The y-intercept is $$(0,4)$$. - Find x-intercept: Set $$y=0$$, then $$2x = 12$$, so $$x = \frac{12}{2} = 6$$. The x-intercept is $$(6,0)$$. 6. Another example: For $$x - 2y = 4$$, - Find x-intercept: Set $$y=0$$, then $$x = 4$$, so intercept is $$(4,0)$$. - Find y-intercept: Set $$x=0$$, then $$-2y = 4$$, so $$y = \frac{4}{-2} = -2$$, intercept is $$(0,-2)$$. 7. To convert to slope-intercept form $$y = mx + b$$, solve for $$y$$: - Example: $$3y = -2x + 12$$ becomes $$y = \frac{-2}{3}x + 4$$, where slope $$m = -\frac{2}{3}$$ and y-intercept $$b = 4$$. 8. Always simplify fractions and show cancellation steps, e.g., $$y = \frac{\cancel{3} \times y}{\cancel{3}} = \frac{-2x + 12}{3}$$. 9. This method helps graph lines and understand their behavior. 10. Practice these steps with different equations to master finding intercepts and slopes.