Writing Linear Equations from a Table
To write the linear equation based on the provided table, we need to determine the slope and the y-intercept of the line.
The slope (m) is the change in y divided by the change in x. Let's calculate it using the values from the table:
m = (change in y) / (change in x)
Looking at the y-values, each time x increases by 1, y decreases by 5 (for example, from -74 to -79, and from -79 to -84, etc.). So, our slope is -5.
Now we need to determine the y-intercept (b), which is the value of y when x is 0. To find the y-intercept, we can use one of the points and the slope to write the equation. Let's take the first point (3, -74).
y = mx + b
-74 = -5(3) + b
To find b, we solve for it:
-74 = -15 + b
b = -74 + 15
b = -59
Now we have both our slope and our intercept. The linear equation in the form y = mx + b is:
y = -5x - 59
This is the equation that represents the rule shown in the table.
