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

2 Answers
May 19, 2015

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#

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 -> b = 4a = 4#

Line passing at point (k, 10)

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