What is the rate of change for the linear relationship modeled in the table? (4 points) x y

-1 10

1 9

3 8

5 7

negative one over two
0
one over two
2

-1/2

Step-by-step explanation:

In a linear relationship, the rate of change of one variable with respect to the other is constant. When we talk about change, we're looking for a difference of values.

If we look at the first and second rows, the change in x is 1 - (-1) = 2, while the change in y is 9 - 10 = -1. Usually we refer to these changes as Δx and Δy (read like "delta-x" and "delta-y"), and the rate of change is the number we get by dividing one of these by the other.

The rate of change we're used to seeing, sometimes called the slope, is Δy/Δx. So, using the values we've already found:

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is