Exercise 6 Page 433

Two beachfront stores rent surfboards. Prices are given in the following table.

We can write the equations for the costs of each store in slope-intercept form. y= mt+ 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/t_2-t_1 In the above formula, (t_1,y_1) and (t_2,y_2) represent pairs of data entries that satisfy the equation.

Equation for Hang Ten

Let's start with the equation for Hang Ten, y=H(t). In order to determine its slope, we will use the coordinate pairs (1,28) and (2,48).

We found out that the slope for H(t) is 20. H(t)= 20t+ b We will now substitute the point (1,28) in the above equation in order to determine the y-intercept b.

The y-intercept is 8. With this, we have everything we need to form an equation for the cost of renting a surfboard from Hang Ten. H(t)= 20t+ 8

Equation for Waverider

We will now write an equation, y=W(t), for Waverider. Let's use (1,46) and (2,63) as our coordinate pairs to determine the slope.

The slope of W(t) is 17. W(t)= 17t+ b Let's find the y-intercept by substituting the point (1,46) in the above equation.

We found the y-intercept to be 29 and thus we can write our second equation. W(t)= 17t+ 29

System of Equations

We will write a system of linear equations using the equations we have written above. H(t)=20t+8 & (I) W(t)=17t+29 & (II) We want to determine the number of hours, t, after which both companies charge the same. To do so, we need to solve the equation H(t)=W(t). H(t)&=W(t) 20t+8&=17t+29 Let's use inverse operations to isolate the t-variable.

Both companies charge same amount for 7 hours of renting a surfboard.