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

Nov 3, 2015

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 $\left(0 , 109.8\right)$

#### Explanation:

Given two points:

$\left({x}_{1} , {y}_{1}\right) = \left(44.2 , - 22.8\right)$

$\left({x}_{2} , {y}_{2}\right) = \left(25.2 , 34.2\right)$

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

$m = \frac{\Delta y}{\Delta x} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{34.2 - \left(- 22.8\right)}{25.2 - 44.2} = \frac{57.0}{-} 19.0 = - 3$

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

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

That is:

$y - \left(- 22.8\right) = - 3 \left(x - 44.2\right)$

That is:

$y + 22.8 = - 3 x + 132.6$

Subtract $22.8$ from both sides to get:

$y = - 3 x + 109.8$

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

So the line intercepts the $y$ axis at $\left(0 , 109.8\right)$