# How do you find the x and y intercepts for a line that goes through (2,1) and (6,4)?

Apr 10, 2018

I'm assuming this is a straight line.

Find the equation of the line. First, find the gradient.

$\frac{4 - 1}{6 - 2} = \frac{3}{4}$

Then substitute values into the equation $y - y 1 = m \left(x - x 1\right)$. I'm going to use (2,1).

$y - 1 = \frac{3}{4} \left(x - 2\right)$

$y - 1 = \frac{3}{4} x - 1.5$
$y = \frac{3}{4} x - 0.5$

Now you know the y-intercept from the equation: $\left(0 , - 0.5\right)$

Now, substitute $y = 0$ into the equation to find the x-intercept

$0 = \frac{3}{4} x - 0.5$
$\frac{3}{4} x = 0.5$
$x = \frac{2}{3}$

The x-intercept is $\left(\frac{2}{3} , 0\right)$