What is the linear equation that gives the rule for this table?y = -5x – 38

To find the linear equation from the given table, we can use the formula for a linear equation in the form of (y = mx + b), where (m) is the slope and (b) is the y-intercept.

1. Finding the slope (m):

Choose two points from the table. For instance, the points (1, -33) and (2, -28).

– The formula for slope (m) is:

[

m = frac{y_2 – y_1}{x_2 – x_1}

]

– Plugging in the values:

[

m = frac{-28 – (-33)}{2 – 1} = frac{5}{1} = 5

]

2. Finding the y-intercept (b):

We can use one of the points and the slope to find (b). Using the point (1, -33):

– Substitute (x) and (y) into the equation:

[

-33 = 5(1) + b

]

– Solving for (b):

[

-33 = 5 + b implies b = -33 – 5 = -38

]

3. Writing the equation:

Now we have (m = 5) and (b