Final answer:
The equation y = mx + b represents a linear relationship where m is the slope and b is the y-intercept. To write an equation from a table, calculate the slope using two points and find the y-intercept either from the table or by calculation.
Step-by-step explanation:
The equation in slope-intercept form is typically written as y = mx + b, where m represents the slope of the line and b denotes the y-intercept. The slope (m) is the rate of change of the line, or how much y changes for a one unit increase in x. The y-intercept (b) is the value of y when x is zero, indicating where the line crosses the y-axis. To write an equation for a given linear relationship, you need two pieces of information: the slope and the y-intercept.
To find the slope, you can use two points from the table and calculate the rise over the run. For the y-intercept, you can either find the point where the line crosses the y-axis in the table or solve for b using the slope and one point from the table.
As an example, if you determine from a table that the slope of the line is 3 and the y-intercept is 9, then the linear equation would be written as y = 3x + 9. This line would rise 3 units for every one unit it runs horizontally, and it would cross the y-axis at 9.