Question

How do you find the y intercept given (44.2, -22.8) and (25.2, 34.2)?

Answer 1

Calculate the slope, hence the equation of the line in point slope form, hence the equation of the line in slope intercept form, hence the intercept `(0, 109.8)`

Explanation:

Given two points:

`(x_1, y_1) = (44.2, -22.8)`

`(x_2, y_2) = (25.2, 34.2)`

The slope `m` of the line through these points is given by the formula:

`m = (Delta y)/(Delta x) = (y_2-y_1)/(x_2-x_1) = (34.2-(-22.8))/(25.2-44.2) = 57.0/-19.0 = -3`

Then we can express the equation of the line in point slope form as:

`y - y_1 = m(x - x_1)`

That is:

`y - (-22.8) = -3(x-44.2)`

That is:

`y + 22.8 = -3x+132.6`

Subtract `22.8` from both sides to get:

`y = -3x+109.8`

This is in slope intercept form, the intercept being `109.8`

So the line intercepts the `y` axis at `(0, 109.8)`