which equation represents the relationship shown in the table below?
x | 0 | 1 | 2 | 3 |
__________________
y | -3 | -1 | 1 | 3 |
a.) y = -x - 3
b.) y = x - 3
c.) y = 2x - 3
d.) y = -2x + 3
To determine the equation that represents the relationship shown in the table, we can use the concept of slope and y-intercept.
First, let's find the slope of the relationship. The slope is the change in y divided by the change in x. Looking at the table, we can see that as x increases by 1, y increases by 2. So, the slope is 2.
Next, let's find the y-intercept. The y-intercept is the value of y when x is equal to 0. From the table, we can see that when x is 0, y is -3. Therefore, the y-intercept is -3.
Now that we know the slope and the y-intercept, we can write the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
Substituting the values, we get the equation y = 2x - 3.
Therefore, the equation that represents the relationship shown in the table is c.) y = 2x - 3.
To determine which equation represents the relationship shown in the table, let's analyze the pattern in the data.
From the table, we can observe that the values of y increase by 2 as x increases by 1. This suggests that the relationship between x and y is a linear relationship.
To find the equation, we can start by looking at the y-intercept, which is the value of y when x is 0. In this case, when x = 0, y = -3.
So, the equation will start with y = ...
Next, we need to determine the slope, which represents the rate at which y changes with respect to x. Since y increases by 2 as x increases by 1, the slope is 2.
Putting this information together, we can conclude that the equation that represents the relationship shown in the table is:
y = 2x - 3
Therefore, option c.) y = 2x - 3 is the correct answer.
Which equation represents the relationship shown in the table?
An x y table is shown. The first row shows negative 4 under column x and negative 3 under y; the second row shows negative 2 and negative 2; the third row shows zero and negative 1; the fourth row shows 2 and zero; the fifth row shows 4 under column x and 1 under column y.