Question 363036
Assume the question is:
A line passes through the points (k+3,-2k) and (4,1) and has a y-intercept of 6.
 Find the value of k.
:
Assign the given points as follows
x1=(k+3); y1=-2k
x2=4; y2=1
:
Find the slope using these points: m = {{{((y2-y1))/((x2-x1))}}}
m = {{{((1-(-2k)))/((4-(k+3)))}}} = {{{((1+2k))/((1-k))}}} is the slope
:
Write the slope intercept form
y = {{{((1+2k))/((1-k))}}}x + 6
Substitute 4 for x and 1 for y; solve for k
{{{((1+2k))/((1-k))}}}(4) + 6 = 1
{{{(4(1+2k))/((1-k))}}} = 1 - 6
{{{((4+8k))/((1-k))}}} = -5
multiply both sides by (1-k), results
4 + 8k = -5(1-k)
4 + 8k = -5 + 5k
8k - 5k = -4 - 4
3k = -9
k + {{{(-9)/3}}}
k = -3
:
Check solution find the value of the 1st pair as given:
(k+3,-2k)
-3+3, -2(-3) = 0, 6