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

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Answer 1 · 2018-04-10T17:04:08

I'm assuming this is a straight line.

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

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

Then substitute values into the equation $y - y 1 = m (x - x 1)$ $y-y1 = m(x-x1)$ . I'm going to use (2,1).

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

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

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

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

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

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