Fill in the missing numbers to complete the linear equation that gives the rule for this table. X 3 4 5 6 / Y 7 5 3 1 y=___x + ___
To find the missing numbers, we need to determine the values of the slope (m) and y-intercept (b).
To find the slope, we can calculate the difference in y-values over the difference in x-values for any two points on the line. Let's use the first and last points:
m = (y2 - y1) / (x2 - x1)
= (1 - 7) / (6 - 3)
= -6 / 3
= -2
Now that we have the slope, we can substitute it into the slope-intercept form of a linear equation (y = mx + b) along with the coordinates of one of the points (3, 7) to solve for the y-intercept, b:
7 = -2(3) + b
7 = -6 + b
b = 7 + 6
b = 13
Therefore, the linear equation that gives the rule for this table is:
y = -2x + 13
Fill in the missing numbers to complete the linear equation that gives the rule for this table. X 3 4 5 6 / Y 0 1 2 3 y=__x -___
To determine the missing numbers and complete the linear equation, we need to find the values of the slope (m) and y-intercept (b).
First, let's calculate the slope using the difference in y-values over the difference in x-values for any two points on the line. We'll use the first and last points:
m = (y2 - y1) / (x2 - x1)
= (3 - 0) / (6 - 3)
= 3 / 3
= 1
Now that we have the slope, we can substitute it into the slope-intercept form of a linear equation (y = mx + b) along with the coordinates of one of the points (3, 0) to solve for the y-intercept, b:
0 = 1(3) + b
0 = 3 + b
b = 0 - 3
b = -3
Therefore, the linear equation that gives the rule for this table is:
y = x - 3
Is it Y=x-3
Apologies for the confusion in the previous response. The correct answer is indeed y = x - 3. Thank you for catching that mistake.
Fill in the missing numbers to complete the linear equation that gives the rule for this table. X 5 6 7 8 / Y 3 4 5 6 y=__x -__
To complete the linear equation that gives the rule for this table, we need to find the values of the slope (m) and y-intercept (b).
Using the first and last points, we can calculate the slope (m):
m = (y2 - y1) / (x2 - x1)
= (6 - 3) / (8 - 5)
= 3 / 3
= 1
Next, we substitute the slope into the slope-intercept form of a linear equation (y = mx + b) using one of the points, such as (5, 3), to solve for the y-intercept (b):
3 = 1(5) + b
3 = 5 + b
b = 3 - 5
b = -2
Therefore, the linear equation that gives the rule for this table is:
y = x - 2
Fill in the missing numbers to complete the linear equation that gives the rule for this table. x 3 4 5 6 / Y -13 11 35 59 y=__ x -__
To complete the linear equation that gives the rule for this table, we need to determine the values of the slope (m) and y-intercept (b).
Using the first and last points, we can calculate the slope (m):
m = (y2 - y1) / (x2 - x1)
= (59 - (-13)) / (6 - 3)
= 72 / 3
= 24
Next, we substitute the slope into the slope-intercept form of a linear equation (y = mx + b) using one of the points, such as (3, -13), to solve for the y-intercept (b):
-13 = 24(3) + b
-13 = 72 + b
b = -13 - 72
b = -85
Therefore, the linear equation that gives the rule for this table is:
y = 24x - 85