Question

A line passes through the points (−200,−4.03×10^4) and (50,9.7×10^3). Find the value of y when x=100. Write your answer in scientific notation.

Answer 1

`y=19.7*10^(3)`

Explanation:

step 1

Find the slope

we know that

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

we have

`(-200,-4.03*10^(4)), (50,9.7*10^(3))`

convert to

`(-200,-40.3*10^(3)), (50,9.7*10^(3))`

substitute in the formula

`m=(9.7*10^(3)+40.3*10^(3))/(50+200)`

`m=(50*10^(3))/(250)`

`m=200`

step 2

Find the equation of the line into point slope form

`y-y1=m(x-x1)`

we have

`(x1,y1)=(50,9.7*10^(3))`

`m=200`

substitute

`y-9.7*10^(3)=200(x-50)` ----> equation of the line into point slope form

step 3

Find the value of y when x=100

substitute in the equation the value of x

`y-9.7*10^(3)=200(100-50)`

`y=200(50)+9.7*10^(3)`

`y=19,700`

`y=19.7*10^(3)`