2.  The steps to follow to solve a problem with direct variation: 1. Write the equation: y = kx 2. Substitute for x and y 3. Solve for k 4. Rewrite the equation substituting the value of k as the constant

3. 1. Write the equationy = kx 2. Substitute for x and y7 = k(35) 3. Solve for k7/35= k, or k = 1/5 4. Rewrite the equation with k y = 1/5x as the constant

4.  y = cost; x = number of hours 1. y = kx 2. 14.40 = k(30) 3. 14.40/30 = k, or k = 0.48  Equation: y = 0.48x

5. 1. y = 28 when x = 7  Equation: y = 4x 2. y = 30 when x = 8  Equation: y = 15/4x 3. y = 400 when x = 125  Equation: y = 16/5x 4. y = 630 when x = 175  Equation: y = 18/5x

6. 5. Follow the steps above:  y = kx  6578 = k(2)  6578/2 = k or 3289  y = 3289x Solve the equation for the new y: y = 3289(5) y = 16,445 The machine can make 16,445 bolts in 5 hours.

7. 5. Or you can set up a direct proportion:  6578/2 = x/5 And solve: 2x = 32,890 2 2  x = 16,445