1. **State the problem:** We need to graph the linear equation $$7y - 3 = -x$$. 2. **Rewrite the equation in slope-intercept form:** The slope-intercept form is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. Start with the given equation: $$7y - 3 = -x$$ Add 3 to both sides: $$7y = -x + 3$$ Divide both sides by 7: $$y = \frac{-x + 3}{7}$$ Show canceling step: $$y = \frac{\cancel{7}(-x + 3)}{\cancel{7}}$$ Simplify: $$y = -\frac{1}{7}x + \frac{3}{7}$$ 3. **Identify slope and intercept:** - Slope $m = -\frac{1}{7}$ - Y-intercept $b = \frac{3}{7}$ 4. **Find x-intercept:** Set $y=0$ and solve for $x$: $$0 = -\frac{1}{7}x + \frac{3}{7}$$ Multiply both sides by 7: $$0 = -x + 3$$ Add $x$ to both sides: $$x = 3$$ 5. **Plot points:** - Y-intercept at $(0, \frac{3}{7})$ - X-intercept at $(3, 0)$ 6. **Draw the line:** Connect these two points with a straight line. The slope $-\frac{1}{7}$ means the line goes down 1 unit for every 7 units it moves to the right. Final answer: The equation in slope-intercept form is $$y = -\frac{1}{7}x + \frac{3}{7}$$ which can be graphed using the intercepts $(0, \frac{3}{7})$ and $(3, 0)$.