Use the table to answer the question.
X Y
4 38
6 58
Write the equation of the linear function that models the relationship shown in the table.
(1 point
O y =10x + 2
O y =x +34
O y=-10x + 78
To write the equation of the linear function, we need to determine the slope (m) and y-intercept (b).
First, calculate the slope using the two points given in the table:
m = (58 - 38) / (6 - 4) = 20 / 2 = 10
Now that we have the slope m = 10, we can use one of the points (4, 38) to find the y-intercept. Substitute the values x = 4, y = 38, and m = 10 into the slope-intercept equation y = mx + b:
38 = 10(4) + b
38 = 40 + b
b = 38 - 40
b = -2
Therefore, the equation of the linear function that models the relationship shown in the table is:
y = 10x - 2
The correct answer is:
y = 10x - 2
Are you sure
I apologize for the confusion in my previous response. Let me re-calculate the slope and y-intercept.
Using the two points from the table (4, 38) and (6, 58), we can calculate the slope:
m = (y₂ - y₁) / (x₂ - x₁)
m = (58 - 38) / (6 - 4)
m = 20 / 2
m = 10
Now that we have the slope m = 10, we can use one of the points (4, 38) to find the y-intercept. Substitute the values x = 4, y = 38, and m = 10 into the slope-intercept equation y = mx + b:
38 = 10(4) + b
38 = 40 + b
b = 38 - 40
b = -2
Therefore, the equation of the linear function that models the relationship shown in the table is:
y = 10x - 2
The correct answer is:
y = 10x - 2
Thank you for pointing out the error.
Is that the correct answer
Yes, the correct equation of the linear function that models the relationship shown in the table is:
y = 10x - 2
I appreciate your diligence in confirming the accuracy of the answer. If you have any more questions or need further clarification, please feel free to ask.