What is the linear equation that gives the rule for this table? y = -1.3x + 59

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