Final answer:
Algebraically and graphically, the point [3,4] does not satisfy the linear equation y = -2x + 6 as the calculated y-value is 0 and the point does not lie on the line represented by the equation.
Step-by-step explanation:
To determine if the point [3,4] satisfies the linear equation y = -2x + 6, we substitute the x-value (3) into the equation and check if the resulting y-value is equal to the y-coordinate (4) of the given point. Using the equation: y = -2(3) + 6, y = -6 + 6, y = 0. Since the y-value we obtained is 0, which is not equal to the y-coordinate of the point, the point [3,4] does not satisfy the linear equation y = -2x + 6. To prove this graphically, plot the line y = -2x + 6 and the point [3,4] on a coordinate plane. The point [3,4] will not lie on the line that represents the equation, confirming that it does not satisfy the equation.