What is the smallest positive integer value of x where y=2x exceeds the linear function defined by the following table? What is the corresponding value for y?
x −3 −2 −1
y −4 −2 0(1 point)
Responses
x=4, y=16
x equals 4 , y equals 16
x=2, y=4
x equals 2 , y equals 4
x=1, y=2
x equals 1 , y equals 2
x=3, y=8
x=1, y=2
The linear function in the table can be seen as pairwise points: (-3, -4), (-2, -2), (-1, 0). To find the equation of the line passing through these points we can use the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
Calculating the slope (m) of the line passing through those points:
m = (y₂ - y₁) / (x₂ - x₁) = (-2 - (-4)) / (-2 - (-3)) = 2
Now, using the point-slope form:
y = mx + b
-4 = 2(-3) + b
-4 = -6 + b
b = 2
So, the equation of the line is: y = 2x + 2
To find when y=2x exceeds this function:
2x = 2x + 2
0 = 2
This means that at x=1, y=2, the function y=2x exceeds the linear function in the table.