1) 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
2) in a relationship between variables, what is the variable called that changes in response to another variable?
A: function
B: input function
C: independent variable
D: dependent variable
since y changes by 2 for each change of 1 in x, look for something like
y = 2x
But since 2*0 = 0, and you want y(0) = -3, the answer is
y = 2x-3
You could have tried all four choices in about 2 minutes if you were unsure.
"in response" means it depends on the other, right?
1) To determine the equation that represents the relationship shown in the table, we can use the values of x and y given.
Looking at the values, we see that as x increases by 1, y also increases by 2. This indicates that there is a linear relationship between x and y, where the slope is 2.
We can observe that when x=0, y=-3. This gives us the y-intercept of the equation.
Using this information, we can determine the equation that represents the relationship. The equation that matches the given data is option C: y=2x-3.
2) In a relationship between variables, the variable that changes in response to another variable is called the dependent variable. Therefore, the correct answer is option D: dependent variable.
1) To determine which equation represents the relationship shown in the table, we need to look for a pattern in the values of x and y.
Looking at the table, we can observe that when the value of x increases by 1, the value of y also increases by 2. This suggests that the relationship between x and y is a linear relationship.
Now, let's examine the given options:
A: y=-x-3
B: y=x-3
C: y=2x-3
D: y=-2x+3
By comparing the relationship in the table to the equations, we can see that the equation C: y=2x-3 matches the pattern. When x is 0, y is -3; when x is 1, y is -1; when x is 2, y is 1; and when x is 3, y is 3.
Hence, the correct equation representing the relationship in the table is C: y=2x-3.
2) In a relationship between variables, the variable that changes in response to another variable is called the dependent variable.
Hence, the correct answer is D: dependent variable.