How do you find the x and y intercepts of a line given 2 points?

Answer 1

The easiest way is to graph it, but if they want it done with algebra, it's a multi-step process. Let's say the points are (2, 3) and (4, 5)

Step one: get the slope

Slope = (y2 - y1) / (x2 -x1) where y1 is the y-coordinate on the first point, and y2 is the y-coordinate on the second point. The same is true for x1 and x2.

Slope = (5 - 3) / (4 - 2) = 1

Step two: plug the slope into the equation for a line: y = mx + b where m is the slope, x is the x-intercept, and b is the y-intercept.

y = (1)x + b

Step three: get the y-intercept (b): to get this, you need to plug in one of the points (it doesn't matter which one) for y and x. Let's take point (2, 3).

3 = (1)(2) + b - notice I replaced y with 3 and x with 2.

Now, solve for b.

3 = 2 + b

b = 1

Step four: Get the x-intercept. The x-intercept is always where y = 0 (0,0), so we plug 0 in for y on the equation using the information we've acquired and solve for x.

0 = (1)x + 1

0 = 1x + 1, or 0 = x + 1

x = -1

Therefore, the x-intercept is -1 and the y-intercept is 1.