Which linear equation is represented by the table?
X: -2, 1 , 3 , 6
Y: 7 , 4 , 2 , -1
A. Y= -x + 5
B. Y= 2x - 1
C. Y= x + 3
D. Y= -3x + 11
I would tell you my answer but I don't even know how to do this so please give me the steps
First you have to find the slope. Do you know how to do this?
I am sorry but no and there is no slope showing in my math proble.
You are given 4 points:
(-2,7), (1,4) , (3,2), and (6,-1)
now see if those points satisfy each of the equations
e.g. let's try (1,4)
in A: 4 = -1+5 , true
in B: 4 = 2(1) - 1 , false , so I guess B is out, no need to go further
continue with the other points.
To determine which linear equation is represented by the table, you can use the method of finding the equation of a line given two points.
Step 1: Select two points from the table. Let's choose (-2, 7) and (3, 2).
Step 2: Calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Using (-2, 7) and (3, 2):
m = (2 - 7) / (3 - (-2))
m = -5 / 5
m = -1
Step 3: Use one of the points and the slope to determine the y-intercept (b) using the formula:
b = y - mx
Using (-2, 7):
b = 7 - (-1)(-2)
b = 7 - 2
b = 5
Step 4: Write the equation in slope-intercept form (y = mx + b) using the values of m and b:
y = -x + 5
Now that we have the equation in slope-intercept form, we can compare it to the options given.
A. Y= -x + 5: This matches the equation we found, y = -x + 5.
B. Y= 2x - 1: This equation does not match the pattern of the given points.
C. Y= x + 3: This equation does not match the pattern of the given points.
D. Y= -3x + 11: This equation does not match the pattern of the given points.
Therefore, the linear equation represented by the table is Y= -x + 5, option A.