# How do you find the y-intercept given (1,2) (3,-4)?

Jul 30, 2015

Find y-intercept of line (1, 2) (3, -4)

Ans: y = 5

#### Explanation:

Equation of the line : y = ax + b where b is the x-intercept.
Write that this line passes at point (1, 2):
2 = a + b --> b = 2 - a.
Write that this line passes at point (3 - 4):
-4 = 3a + b = 3a + 2 - a --> 2a = - 6 --> $a = - 3$--> b = 2 + 3 = 5.
To find y-intercept, make x = 0 --> y = b = 5.

Jul 30, 2015

Here is another way to arrive at the correct answer. The $y$ intercept is $5$ (or, $\left(0 , 5\right)$ if you prefer giving both coordinates.)

#### Explanation:

If you think of the answer as our destiniation, then, like in the physical world of travel, there are often many routes you might take to get to the same destination.

Given the points: $\left(1 , 2\right)$ and $\left(3 , - 4\right)$ we can find the #y intercept by first finding an equation for the line.

The slope is $m = \left(- 4 - 2\right) , \left(3 - 1\right) = - \frac{6}{2} = - 3$

So one equation for the line is:

$y - 2 = - 3 \left(x - 1\right)$

If we solve for $y$, we will have the slope-intercept equation for the line:

$y - 2 = - 3 x + 3$

$y = - 3 x + 5$

The $y$ intercept is $5$.

Alternative Method

When we get $y - 2 = - 3 \left(x - 1\right)$, we can find the $y$ intercept by making $x = 0$, so we have:

$y - 2 = - 3 \left(0 - 1\right) = 3$, and

$y = 5$ for the intercept.