SOLUTION: Determine the equation of a lineˏ in slope-intercept formˏ that passes through the points (6, 1) and (-10, 9) a.) y= -1/2x + 4 b.) y= -1/2x - 2 c.) y= -2x + 8 d.)

Algebra ->  Linear-equations -> SOLUTION: Determine the equation of a lineˏ in slope-intercept formˏ that passes through the points (6, 1) and (-10, 9) a.) y= -1/2x + 4 b.) y= -1/2x - 2 c.) y= -2x + 8 d.)      Log On


   

Question 944988: Determine the equation of a lineˏ in slope-intercept formˏ that passes through the points (6, 1) and (-10, 9)
a.) y= -1/2x + 4
b.) y= -1/2x - 2
c.) y= -2x + 8
d.) y= -2x+ 13
Found 2 solutions by josmiceli, MathLover1:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The slope is ( change in y ) / ( change in x )
Let slope = +m+
+m+=+%28+9+-+1+%29+%2F+%28+-10+-+6+%29+
+m+=+8+%2F+%28-16%29+
+m+=+-1%2F2+
----------------
Use the general point-slope formula
+%28+y+-+1+%29+%2F+%28+x+-+6+%29+=+-1%2F2+
+y+-+1+=+-%281%2F2%29%2A%28+x+-+6+%29+
+y+-+1+=+-%281%2F2%29%2Ax+%2B+3+
+y+=+-%281%2F2%29%2Ax+%2B+4+
The answer is (a)

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
the equation of a line in slope-intercept form:
y=mx%2Bb where m is a slope and b y-intercept
we will use given points (6,+1) and (-10, 9) to set up system and solve it for m and b

y=mx%2Bb if (6,+1) then we have
1=m%2A6%2Bb
1=6m%2Bb.....eq.1
y=mx%2Bb if (-10,+9) then we have
9=m%2A%28-10%29%2Bb
9=-10m%2Bb.....eq.2
so, the system is:
1=6m%2Bb.....eq.1
9=-10m%2Bb.....eq.2
----------------------------------
start with 1=6m%2Bb.....eq.1, solve for b
1-6m=b...substitute in eq.2

9=-10m%2B1-6m.....eq.2, solve for m
9-1=-16m
8=-16m
16m=-8
m=-8%2F16
m=-%281%2F2%29

now find b
b=1-6m
b=1-6%28-1%2F2%29
b=1-cross%286%293%28-1%2Fcross%282%29%29
b=1-3%28-1%29
b=1%2B3
b=4
so, your equation is: y=-%281%2F2%29x%2B4
and your answer is a.)