ethan tried to write an equation of the linear table but made a mistake
x: 2,4,6
y:-2, 0,2
y=x+4
what is the correct solution?
explain ethans mistake in the box below
Ethan's mistake is that he assumed y would always be equal to x + 4. However, if we observe the given table, we can see that when x = 2, y = -2. This means that y is not always equal to x + 4. So, Ethan's equation of y = x + 4 is incorrect.
To find the correct equation, we can calculate the difference in y-values and divide it by the difference in x-values.
When x increases by 2 units (from 2 to 4), y increases by 2 units (from -2 to 0).
Similarly, when x increases by 2 units (from 4 to 6), y increases by 2 units (from 0 to 2).
Therefore, the difference in y-values is 2, and the difference in x-values is 2.
So, the slope (m) of the linear relation is 2/2 = 1.
Now, we can use the point-slope form of a linear equation to find the correct equation.
Using the point (2, -2) and the slope m = 1, the equation can be written as:
y - y₁ = m(x - x₁)
where x₁ = 2 and y₁ = -2 are the coordinates of the given point.
Plugging in the values, we have:
y - (-2) = 1(x - 2)
y + 2 = x - 2
Subtracting 2 from both sides, we get:
y = x - 4
Therefore, the correct equation for the given table is y = x - 4.