look at this table:
x
-6, -5, -4, -3, -2
y
-34, -30, -26, -22, -18
write a linear function (y=mx+b) or an exponential function (y=a(b)^) that models the data.
y=
what is the answer ?
To find the equation that models the data, we first need to determine whether the relationship between the x and y values is best represented by a linear function (y = mx + b) or an exponential function (y = a(b)^x).
Based on the given table of values, it appears that a linear function would be the best fit, as the change in the y values does not seem to increase exponentially with each decrease in x value.
To find the linear function that models the data, we can calculate the slope (m) and y-intercept (b) using two of the given points (-6, -34) and (-5, -30):
m = (y2 - y1) / (x2 - x1)
m = (-30 - (-34)) / (-5 - (-6))
m = -4 / 1
m = -4
Next, we can substitute the slope (-4) and one of the points into the equation y = mx + b to find the y-intercept (b):
-30 = (-4)(-5) + b
-30 = 20 + b
b = -50
Therefore, the linear function that models the data is:
y = -4x - 50
are you sure?
Apologies for the mistake in the previous calculation. Let's correct that:
Given points are (-6, -34) and (-5, -30).
To find the linear function:
1. Calculate Slope (m):
m = (y2 - y1) / (x2 - x1)
m = (-30 - (-34)) / (-5 - (-6))
m = (-30 + 34) / (-5 + 6)
m = 4 / 1
m = 4
2. Using the point (-6, -34):
y = mx + b
-34 = 4(-6) + b
-34 = -24 + b
b = -34 + 24
b = -10
Therefore, the correct linear function that models the data is:
y = 4x - 10