130k views
2 votes
The table represents some points on the graph of a linear function.

EK 5 31 45
y 3 3 22 15
Which equation represents the same relationship?
A. 2y - 1 = 0
B. 2x - y + 7 = 0
C. y - 3 = 1/2(x - 5)
D. y - 15 = 2(x - 31)

User Darxsys
by
7.8k points

1 Answer

2 votes

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.

User CAMOBAP
by
8.1k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories