Exercise 5 Page 433

We have two garden supply companies that deliver pea stones, each with different prices for different numbers of cubic yards.

We can write the equations for the costs of each company in slope-intercept form. y= mx+ b In this form, m is the slope and b is the y-intercept. We will find each slope by using the Slope Formula. m=y_2-y_1/x_2-x_1 In the above formula, (x_1,y_1) and (x_2,y_2) represent pairs of data entries that satisfy the equation.

Equation for Yard Depot

Let's start with the equation for Yard Depot, y=Y(x). In order to determine its slope, we will use the coordinate pairs (1,75) and (2,110).

Thus, the slope for Y(x) is 35. Y(x)= 35x+ b We will now substitute the point (1,75) in the above equation in order to determine the y-intercept b.

The y-intercept is 40. With this, we have everything we need to form an equation for the cost of pea stones from Yard Depot. Y(x)= 35x+ 40

Equation for Lawn & Garden

We will now write an equation, y=L(x), for Lawn & Garden. Let's use (1,45) and (2,85) as our coordinate pairs to determine the slope.

The slope of L(x) is 40. L(x)= 40x+ b Let's find the y-intercept by substituting the point (1,45) in the above equation.

We found the y-intercept to be 5 and thus we can write our second equation. L(x)= 40x+ 5

System of Equations

We will write a system of linear equations using the equations we have written above. Y(x)=35x+40 & (I) L(x)=40x+5 & (II) We want to determine the amount of pea stones, x, for which both companies charge the same. To do so, we need to solve the equation Y(x)=L(x). Y(x)&=L(x) 35x+40&=40x+5 Let's use inverse operations to isolate the x-variable.

Both companies charge same amount for 7 cubic yards of pea stone.