Final answer:
The function f(x)=-2x+6 represents a straight line with a negative slope that crosses the y-axis at (0,6). The slope indicates that for every unit increase in x, the value of y decreases by 2, creating a consistent downward trend to the right on the graph.
Step-by-step explanation:
The chart that could represent the function f(x)=-2x+6 would have specific characteristics based on the given linear equation.
Firstly, this function represents a straight line with a negative slope, as indicated by the coefficient of x, which is -2.
The y-intercept of this function is +6, meaning the line will cross the y-axis at the point (0,6).
To visualize this function as a graph, we would plot the y-intercept and then use the slope to determine the direction and steepness of the line.
For every unit increase in x, y would decrease by 2 units, showing a consistent downward trend to the right.
The line extends infinitely in both directions, but the chart or graph you present would only show a segment based on the range or domain you choose to display.
A common method to further illustrate this is to pick two points that satisfy the equation and plot these on the Cartesian plane.
For example, using the points (0,6) for the y-intercept and (3,0), where x equals 3 and f(3) equals 0, would suffice to define the line graphically.
Connect these points with a straight line, and you have the graph of the function.
The complete quetion is:Which chart could represent the function f(x)=-2x+6