Final answer:
To identify the correct equation that represents the same relationship as the given linear function, test the points in the table against each equation option. Look for the slope and y-intercept in the equation that matches the pattern seen in the points' values.
Step-by-step explanation:
To find which equation from the options provided represents the same relationship as a given linear function, we can test the given points against each equation. The table with points (1,5), (2,10), (3,7), and (4,14) gives us pairs of x and y values that must satisfy the correct equation.
An equation of a linear function typically has the form y = mx + b, where m is the slope and b is the y-intercept. By examining the given points, we can determine the slope (change in y divided by change in x) and use one of the points to solve for the y-intercept.
Let's implement this on an example equation y = 9 + 3x. Here, the 'm' term represents the slope which is 3, and the 'b' term represents the y-intercept which is 9. If you plug in different x values into this equation, calculate y, and then plot these points on a graph, you'll get a straight line representing this linear relationship. This relationship showcases the dependence of y on x.
To choose the correct equation from the options, you would need to substitute the x and y values from the given points into each equation and see if the equation holds true.