Question

As spring has sprung, Thomas decides to over seed his lawn. After 3 weeks of spreading grass there are 5,250 blades of grass. After 7 weeks there are 5,952 blades of grass. Write an equation to represent this situation.

Answer 1

Let weeks be x and blades be y ,form two coordinates

• (3,5250)
• (7,5952)

Find slope

• m=5952-5250/7-3
• m=702/4=351/2

Equation in point slope form

• y-5250=351/2(x-3)
• y-5250=351/2x-1053/2
• y=351/2x-1053/2+5250
• y=351/2x+9447/2

Answer 2

• y = 175.5x + 4723.5

Explanation:

Use the pairs of values as coordinates and make a linear equation based on this.

• y = mx + b, the linear equation in slope-intercept form

The pairs are (3, 5250) and (7, 5952).

Find the slope:

• m = (5952 - 5250)/(7 - 3) = 702/4 = 175.5

Find the y- intercept:

• 5250 = 3*175.5 + b
• 5250 = 526.5 + b
• b = 5250 - 526.5
• b = 4723.5

The equation is

• y = 175.5x + 4723.5

y - blades of grass after x weeks, x - number of weeks passed since spreading the grass