Subjects algebra

Vertical Line 8F9120

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1. **State the problem:** We need to find the gradient (slope) of the linear equation $8x + 6 = 22$ and represent it in slope-intercept form. 2. **Rewrite the equation:** Start by isolating $x$. $$8x + 6 = 22$$ 3. **Subtract 6 from both sides:** $$8x + \cancel{6} - \cancel{6} = 22 - 6$$ $$8x = 16$$ 4. **Divide both sides by 8 to solve for $x$:** $$\frac{8x}{\cancel{8}} = \frac{16}{\cancel{8}}$$ $$x = 2$$ 5. **Interpretation:** The equation $8x + 6 = 22$ simplifies to $x = 2$, which is a vertical line. Vertical lines have an undefined gradient. 6. **Gradient:** The gradient (slope) of the line $x=2$ is undefined. 7. **Slope-intercept form:** Since the line is vertical, it cannot be represented in the form $y = mx + c$ (slope-intercept form) because the slope $m$ is undefined. 8. **Summary:** The line $8x + 6 = 22$ is vertical at $x=2$ with an undefined gradient and cannot be expressed as $y = mx + c$.