Final answer:
To write a linear equation that represents the scenario, we need to find the equation in the form of y = mx + b. Given the square footage of 1100 and the rent of $1125, we can plug these values into the equation to find the slope and the y-intercept.
Step-by-step explanation:
To write a linear equation that represents the scenario, we need to find the equation in the form of y = mx + b.
Let x represent the square footage of the office and y represent the rent.
Given that the office has a square footage of 1100 and the rent is $1125, we can plug these values into the equation to find the slope (m) and the y-intercept (b).
Using the point-slope form of a linear equation, we have:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line.
Substituting the values:
1125 - y1 = m(1100 - x1)
Since we're given the rent (y) and the square footage (x), we can rearrange the equation to solve for m:
1125 - y1 = 1100m - mx1
Now we can find the slope:
m = (1125 - y1 + mx1) / 1100
Finally, we can use the given information to solve for the y-intercept (b) using the slope-intercept form of a linear equation:
y = mx + b
Plugging in the values:
1125 = m(1100) + b
We can now substitute the slope (m) we found earlier:
1125 = ((1125 - y1 + mx1) / 1100)(1100) + b
Now we have the linear equation that represents the scenario.