X|-2|0|2|4|
Y|-4|0|4|8|
Do the values in the table represent a linear function? If so what is the function rule?
A. The values do not show a linear function.
B. Yes, the values show a linear function; y=1/2x+4.
C. Yes,the values show a linear function; y=2x+2.
D. Yes, the values show a linear function; y=2x.
Is the answer B?
How did you decide it was B ?
Watch x and y values :
x = - 2 , y = - 4 , y = 2 x
x = 0 , y = 0 , y = 2 x
x = 2 , y = 4 , y = 2 x
x = 4 , y = 8 , y = 2 x
y = 2 x
How does y equal 2x
To determine if the values in the table represent a linear function, you need to check if there is a consistent linear relationship between the x-values and the y-values.
Looking at the x-values (-2, 0, 2, 4) and the corresponding y-values (-4, 0, 4, 8), we can see that for every increase of 2 in the x-values, the y-values increase by 4. This consistent rate of change suggests that the values do represent a linear function.
To find the function rule, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope and b represents the y-intercept.
To find the slope (m), we can choose any two points from the table and use the formula:
m = (change in y) / (change in x)
Let's choose the points (0,0) and (2,4):
m = (4 - 0) / (2 - 0)
m = 4 / 2
m = 2
So, the slope (m) is 2.
Next, we need to find the y-intercept (b) by substituting the values of one point (x, y) into the equation.
Using the point (0,0):
0 = 2(0) + b
0 = b
Therefore, the y-intercept (b) is 0.
Putting it all together, the function rule for the given values is y = 2x + 0, which simplifies to y = 2x.
So, the correct answer is D. Yes, the values show a linear function; y = 2x.