Question

Lizzy is tiling a kitchen floor for the first time. She had a tough time at first and placed only 1 tile the firstday. She started to go faster and by the end of day 4, she had placed 31 tiles. She worked at a steady rate after the first day. Use an equation in point-slope form to determine how many days Lizzy took to place all of the 100 tiles needed to finish the floor. Solve the problem using an equation in point-slope form.Lizzy took______days to place all the tiles. Ok so I was working on this and I have y-1=10(x-1) is this correct so far and what do I do next?

Answer 1

Equation: y - 1 = 10( x - 1)

Step-by-step explanation:

If we call x the number of days and y the number of tiles placed, then the word problem gives us two points that lie on the line we are trying to find the equation for. These points are (1,1) and (4, 31).

First, we find the slope of the line. The slope is found by dividing the difference in y coordinates by the difference in x -coordinates.

`m=(31-1)/(4-1)=(30)/(3)`
`\boxed{m=3.}`

With the value of the slope in hand, we now use the point (1,1) to write the point-slope equation of the line.

`\boxed{y-1=10\mleft(x-1\mright)_{}}`

With this equation in hand, now let us find how many days it will take Lizzy to place 100 tiles. To find out we substitute y = 100 into the above equation and solve for x.

`100-1=10(x-1)`
`\Rightarrow99=10(x-1)`

dividing both sides by 10 gives

`9.9=x-1`

finally, adding 1 to both sides gives

`x=9.9+1`
`\boxed{x=10.9.}`

which is about 11 days.

Hence, it took lizzy exactly 10.9 days to place all the tiles.