Mr. Simon landscapes new houses for a building contractor. He charges by the square meter of yard space plus a setup fee. He billed the contractor $2,150 for a 400-square- meter yard and $1,650 for a 300-square-meter yard. Write an equation in the form
y = mx + b that can be used to find the cost, y, to landscape any amount of yard space, x.\
400m+b = 2150
300m+b = 1650
subtract to get
100m = 500
m = 5
so, b = 150
y = 5x+150
To write the equation in the form y = mx + b, where y represents the cost of landscaping, x represents the amount of yard space, m represents the cost per square meter, and b represents the setup fee, we need to find the values of m and b.
Let's start by finding the cost per square meter, m.
From the given information, we know that Mr. Simon billed $2,150 for a 400-square-meter yard and $1,650 for a 300-square-meter yard.
We can set up two equations based on this information:
1) 2150 = m * 400 + b
2) 1650 = m * 300 + b
Simplifying these equations, we get:
1) 400m + b = 2150
2) 300m + b = 1650
Now we can solve this system of equations to find the values of m and b.
Subtracting equation 2 from equation 1 eliminates the b term:
(400m + b) - (300m + b) = 2150 - 1650
100m = 500
m = 500/100
m = 5
Substituting the value of m into equation 1:
400(5) + b = 2150
2000 + b = 2150
b = 2150 - 2000
b = 150
Therefore, the equation in the form y = mx + b that can be used to find the cost, y, to landscape any amount of yard space, x, is:
y = 5x + 150