x: -2 -1 2 5 y: 80 70 40 10
What is the slope of the line?
What is the y-intercept of the line?
What is the equation of the line?
-10
10
-30
30
(0,10)
(0,30)
(0,60)
y = 10x - 30
y = -30x + 10
y = -10x + 60
To find the slope of the line, we need to use the formula:
slope = (y2 - y1) / (x2 - x1)
Let's use the first two points (-2,80) and (-1,70) to calculate the slope:
slope = (70 - 80) / (-1 - (-2))
slope = (-10) / 1
slope = -10
So the slope of the line is -10.
To find the y-intercept of the line, we can substitute one of the points into the equation and solve for b in the equation y = mx + b. Let's use the point (-2,80):
80 = -10(-2) + b
80 = 20 + b
b = 80 - 20
b = 60
So the y-intercept of the line is 60.
Therefore, the equation of the line is y = -10x + 60.
Table 1: x: -4 -2 0 2 4 f (x): -10 -8 -6 -4 -2
Table 2: x: 4 -2 0 2 4 f (x): 256 16 0 16 256
Table 3: x: -4 -2 0 2 4 f (x): -8 -4 0 4 8
Table 4: x: -4 -2 0 2 4 f (x): -1 1 3 5 7
Table 5: x: -4 -2 0 2 4 f (x): 3 5 7 9 11
Which of these tables DOES NOT represent a linear function?
A linear function is a function that can be represented by a straight line. In a linear function, the relationship between the independent variable (x) and the dependent variable (f(x)) is constant.
Looking at the tables provided:
- Table 1: The relationship between x and f(x) changes by -2 for every 1 unit change in x. This is a linear function.
- Table 2: The relationship is not constant, as we see that the f(x) values are not changing by a constant rate. This does not represent a linear function.
- Table 3: The relationship between x and f(x) changes by 4 for each 1 unit change in x. This is a linear function.
- Table 4: The relationship between x and f(x) changes by 2 for each 1 unit change in x. This is a linear function.
- Table 5: The relationship between x and f(x) changes by 2 for every 1 unit change in x. This is a linear function.
Therefore, Table 2 does not represent a linear function, as the f(x) values are not changing at a constant rate.