Final answer:
The graph of the line y = -2(3 – 5) + 4 is a horizontal line passing through the y-axis at y = 8.
Step-by-step explanation:
To graph the line y = -2(3 – 5) + 4, we first simplify the expression within the parentheses: 3 – 5 = -2. Substituting this back into the original equation, we get y = -2(-2) + 4. Further simplifying, we have y = 4 + 4, which equals y = 8. This implies that every point on the line has a y-coordinate of 8. Since there's no variable affecting the y-coordinate, the line is horizontal.
Graphically, the line is a horizontal line parallel to the x-axis, intersecting the y-axis at y = 8. The slope of the line is 0, as it doesn't rise or fall. All points on the line have a constant y-coordinate of 8, making it a straightforward horizontal stretch. This type of equation represents a constant function, where the output (y) is always the same, regardless of the input (x).
In summary, the graph of y = -2(3 – 5) + 4 is a horizontal line situated at y = 8. It does not depend on the value of x, creating a constant function that remains consistent along the y-axis.