if x=-4,-4,-4,-4 and y=0,1,2,3 in a graph. find the equation for it
Answers
Answer:
The equation d = 40f pairs a distance d for each time t. For example,
if t = 1, then d = 40
if t = 2, then d = 80
if t = 3, then d = 120
and so on.
The pair of numbers 1 and 40, considered together, is called a solution of the equation d = 40r because when we substitute 1 for t and 40 for d in the equation, we get a true statement. If we agree to refer to the paired numbers in a specified order in which the first number refers to time and the second number refers to distance, we can abbreviate the above solutions as (1, 40), (2, 80), (3, 120), and so on. We call such pairs of numbers ordered pairs, and we refer to the first and second numbers in the pairs as components. With this agreement, solutions of the equation d - 40t are ordered pairs (t, d) whose components satisfy the equation. Some ordered pairs for t equal to 0, 1, 2, 3, 4, and 5 are
(0,0), (1,40), (2,80), (3,120), (4,160), and (5,200)
Such pairings are sometimes shown in one of the following tabular forms.
In any particular equation involving two variables, when we assign a value to one of the variables, the value for the other variable is determined and therefore dependent on the first. It is convenient to speak of the variable associated with the first component of an ordered pair as the independent variable and the variable associated with the second component of an ordered pair as the dependent variable. If the variables x and y are used in an equation, it is understood that replace- ments for x are first components and hence x is the independent variable and replacements for y are second components and hence y is the dependent variable. For example, we can obtain pairings for equation
by substituting a particular value of one variable into Equation (1) and solving for the other variable.
Example 1
Find the missing component so that the ordered pair is a solution to
2x + y = 4
a. (0,?)
b. (1,?)
c. (2,?)
Solution
if x = 0, then 2(0) + y = 4
y = 4
if x = 1, then 2(1) + y = 4
y = 2
if x = 2, then 2(2) + y = 4
y = 0
The three pairings can now be displayed as the three ordered pairs
(0,4), (1,2), and (2,0)
or in the tabular forms
EXPRESSING A VARIABLE EXPLICITLY
We can add -2x to both members of 2x + y = 4 to get
-2x + 2x + y = -2x + 4
y = -2x + 4
In Equation (2), where y is by itself, we say that y is expressed explicitly in terms of x. It is often easier to obtain solutions if equations are first expressed in such form because the dependent variable is expressed explicitly in terms of the independent variable.
For example, in Equation (2) above,
if x = 0, then y = -2(0) + 4 = 4
if x = 1, then y = -2(1) + 4 = 2
if x = 2 then y = -2(2) + 4 = 0
We get the same pairings that we obtained using Equation (1)
(0,4), (1,2), and (2,0)
We obtained Equation (2) by adding the same quantity, -2x, to each member of Equation (1), in that way getting y by itself. In general, we can write equivalent equations in two variables by using the properties we introduced in Chapter 3, where we solved first-degree equations in one variable.
Step-by-step explanation: