Question

Find the equation of the linear function represented by the table y 6 9 12 15 x 1 2 3 4​

Answer 1

Answer: y = 3x + 3

Step-by-step explanation:

We know the linear function as following:

y = mx + b

m is the slope of the equation. b represents the y-intercept.

To find m, we divide the rate of change of y by the rate of change of x. We know that the rate of change y is +3 because we add three each time in order to find the next value. The rate of change of x is +1 because we add one each time to find the next value. So m would be:

m = 3/1

m = 3

Our linear equation is now as following:

y = 3x + b

In order to find b, we should first substitute a coordinate in the equation above.

y = 3x + b

6 = 3(1) + b

Then, we multiply 3 with 1

6 = 3 + b

Finally, we substract 3 on both sides. Now we've got our b value.

b = 3

Now our equation should look like this.

y = 3x + 3

To verify if the equation, we should substitute another coordinate, and verify if each side of the equation is equal.

y = 3x + 3

15 = 3(4) + 3

15 = 12 + 3

15 = 15

So we now know that the equation is indeed correct.

Answer 2

Answer:

• y = 3x + 3

Step-by-step explanation:

As per given table we have ordered pairs:

• (1, 6), (2, 9), (3, 12), (4, 15)

Find the slope and y- intercept to work out the equation.

• y = mx + b

The slope:

• m = (9 - 6)/(2 - 1) = 3/1 = 3

The y -intercept:

• 6 = 3*1 + b
• 6 = 3 + b
• b = 3

The equation is:

• y = 3x + 3

The graph is attached