ethan trieed to write an equation of the liner table butmade a mistake
x: 2,4,6
Y:-2,0,2
y=x+4
WHat is the correct solution?
explaINS ETHAN MISTAKE INT HE BOX BE;LOW
Ethan's mistake: Ethan made a mistake by taking the values of x and y from the table and assuming they form a linear relationship. However, when we substitute the given values into y = x + 4, we can see that the equation does not hold true for some of the points in the table.
Correct solution: To find the correct equation for the linear relationship of the given table, we can calculate the slope (m) using any two points from the table. Let's choose the points (2, -2) and (6, 2) to calculate the slope:
m = (y2 - y1) / (x2 - x1)
m = (2 - (-2)) / (6 - 2)
m = 4 / 4
m = 1
Now that we have the slope, we can choose any point from the table to substitute into the point-slope form of a linear equation, y - y1 = m(x - x1). Let's choose the point (2, -2):
y - (-2) = 1(x - 2)
y + 2 = x - 2
y = x - 2 - 2
y = x - 4
Therefore, the correct equation for the linear relationship in the given table is y = x - 4.