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

May 19, 2015

Here are two approaches:

Method 1

Given that $x$-intercept is $- 4$, we know that the point $\left(- 4 , 0\right)$ in on the line, as is $\left(2 , 6\right)$. 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 $\left(2 , 6\right)$ to $\left(k , 10\right)$, we need to add $4$ to the $y$ coordinate, so we must also add $4$ to the $x$ coordinate.

$k = 2 + 4 = 6$

May 19, 2015

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 -> $a = 1 \to b = 4 a = 4$

Line passing at point (k, 10)

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