1. **Stating the problem:** Given the straight line AB with equation $y = 2x + 6$, find the equation of a straight line parallel to AB that passes through point $P(6,4)$. 2. **Formula and rules:** - The slope of the line $y = mx + c$ is $m$. - Lines that are parallel have the same slope. - The equation of a line with slope $m$ passing through point $(x_1,y_1)$ is given by: $$y - y_1 = m(x - x_1)$$ 3. **Identify slope of AB:** The given line is $y = 2x + 6$, so the slope $m = 2$. 4. **Use the point-slope form for the new line:** Using point $P(6,4)$ and slope $m=2$: $$y - 4 = 2(x - 6)$$ 5. **Simplify the equation:** $$y - 4 = 2x - 12$$ 6. **Add 4 to both sides:** $$y = 2x - 12 + 4$$ 7. **Simplify the right side:** $$y = 2x - 8$$ **Final answer:** The equation of the line parallel to $AB$ passing through $P(6,4)$ is: $$y = 2x - 8$$