Write the linear equation that gives the rule for this table.
x
-53
-40
-27
-14
y
97
84
71
58
Write your answer as an equation with y first, followed by an equals sign.
What is the linear equation that gives the rule for this table? y = -1.3x + 59
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To find the linear equation that describes the given values of x and y, we can first look for a pattern in the change of values.
1. Identify Changes in y:
– From 97 to 84: decrease of 13 (84 – 97)
– From 84 to 71: decrease of 13 (71 – 84)
– From 71 to 58: decrease of 13 (58 – 71)
The y-values decrease by 13 as x increases by 13 (i.e., -53 to -40, -40 to -27, -27 to -14).
2. Calculate the slope (m):
The slope ( m ) is calculated as the change in y divided by the change in x:
[
m = frac{text{Change in y}}{text{Change in x}} = frac{-13}{13} = -1
]
3. Find the y-intercept (b):
To find the y-intercept, we can substitute one of the points into the equation ( y = mx + b ). Using the point (-53, 97):
[
97 = -1(-53) + b \
97 = 53 + b \
b = 97 – 53 = 44
]
4. Write the Equation:
Now we have both