Question

A line passes through the points (−200, 2.04 × 10^4) and (100, −9.6 × 10^3). Find the value of y when x=300. Write your answer in scientific notation.

Answer 1

y = -29.6 x 10³

Explanation:

First of all, we know that the formula to calculate the slope between two points is equal is given by;

m = {y2-y1}/{x2-x1}

Now, we have the coordinates as;

(−200, 2.04 × 10⁴) and (100, −9.6 × 10³)

Thus; rearranging the first one, we now have;

(−200, 20.4 × 10³) and (100, −9.6 × 10³)

Thus;

m = {(-9.6 x 10³) - (20.4 x 10³)}/{100 - (-200)}

m = (-30 x 10³)/300

m = -100

Now, let's find the equation of the line into point slope form;

y - y1 = m(x - x1)

We have (x1, y1) = (−200, 2.04 × 10⁴)

Thus;

y - (2.04 x 10⁴) = -100(x - (-200))

y - (2.04 x 10⁴) = -100(x + 200)

We want to find the value of y when x=300

Thus;

y - (2.04 x 10⁴) = -100(300 + 200)

y - 20400 = -100(500)

y - 20400 = -50000

y = 20400 - 50000

y = -29,600 = -29.6 x 10³