linear equation

Question

the monthly rent for an 800 square foot office is $975. for an 1100 square foot office rent is 1125. write a linear equation

Answer 1

An 800 square foot office costs $975. Think of this as an ordered pair (800, 975), when x = 800, y = 975.

Similarly, when x = 1100, y = 1125 (1100, 1125). Given that the relationship between x and y is linear, determine the slope of the line passing through those points:

m = (1125 - 975) / (1100 - 800) = 150/300 = 1/2

Pick one of the two points along with the slope, and use the point-slope formula to write the equation of the line, then if you want convert to slope-intercept:

y - 975 = (1/2)( x - 800)

y = (1/2)x - 400 + 975

y = (1/2)x + 575

Check it out here (right click the link and choose "go to..." from the drop-down menu.:

desmos.com/calculator/lkkn8of57l

Note that you could also determine the equation by starting with

y = mx + b (substituting 1/2 for m, 800 for x, 975 for y, and determining the value for b)

975 = (1/2)(800) + b

b = 975 - 400

b = 575

So,

y = (1/2)x + 575