The graph shows the location of all solutions for some linear equation. The coordinates of two of the points are labeled. Which linear equation matches this graph?
A)
x + y = 6
B)
y = 2x + 4
3x + y - 9
D
y = -2(x - 5) -6

Option D

Step-by-step explanation:

Let the equation of the line given in the graph is,

y = mx + b

Here, m = Slope of the line

b = y-intercept

From the graph attached,

y-intercept = 4

Since, slope of the line passing through two points and is given by,

m =

Therefore, slope of the line passing through (-2, 8) and (5, -6) will be,

m =

m =

m = -2

Therefore, equation of the line will be,

y = -2x + 4

Equations given in the options A, B, and C are not matching with our equation.

Simplify the equation given in Option D,

y = -2(x - 5) -6

y = -2x + 10 - 6

y = -2x + 4

Therefore, Option D is the answer.

The crop yield increased by 9 pounds per acre from year 1 to year 10.

Step-by-step explanation:

To solve this we are using the average rate of change formula: , where:

is the second point in the function

is the first point in the function

is the function evaluated at the second point

is the function evaluated at the first point

We know that the first point is 1 year and the second point is 10 years, so and . Replacing values:

Since represents the number of pounds per acre and the number of years, we can conclude that the crop yield increased by 9 pounds per acre from year 1 to year 10.