Question

A line with x-intercept -4 passes through (2,6) and (k,10). How do you find k?

Answer 1

Here are two approaches:

Method 1

Given that `x`-intercept is `-4`, we know that the point `(-4,0)` in on the line, as is `(2,6)`. Find the equation of the line through these two points, then put in `10` for `y` and solve for `x = k`

Method 2
As we work through method 1, we notice that the slope of the line is `1`.

That tells us that increases in `x` and `y` are equal on this line. To get from `(2,6)` to `(k,10)`, we need to add `4` to the `y` coordinate, so we must also add `4` to the `x` coordinate.

`k=2+4=6`

Answer 2

Standard equation of the line : y = ax + b. First find a and b.

x-intercept -4 gives -> y = -4a + b = 0 -> b = 4a (1)

Line passing at point (2, 6):

6 = 2a + b (2) -> 6 = 2a + 4a = 6a -> `a = 1 -> b = 4a = 4`

Line passing at point (k, 10)

10 = ka + b (3) -> 10 = k + 4 -> `k = 10 - 4 = 6`