SOLUTION: What is the equation of a line with points (3,4) and (11,18). After that I need the intersection of that line and line y=-3/2x +12. Thank you.

Question 360551: What is the equation of a line with points (3,4) and (11,18). After that I need the intersection of that line and line y=-3/2x +12. Thank you.
Found 2 solutions by nerdybill, checkley77:
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
What is the equation of a line with points (3,4) and (11,18). After that I need the intersection of that line and line y=-3/2x +12.
.
Slope of (3,4) and (11,18)
m = (18-4)/(11-3) =14/8 = 7/4
.
Using one point (3,4) and the slope 7/4, plug into "point-slope" form:
y - y1 = m(x - x1)
y - 4 = 7/4(x - 3)
y - 4 = (7/4)x - 21/4
y = (7/4)x - 21/4 + 4
y = (7/4)x - 21/4 + 16/4
y = (7/4)x - 5/4
.
Intersection:
(7/4)x - 5/4 = -3/2x +12
multiply both sides by 4:
7x - 5 = -6x + 48
13x - 5 = 48
13x = 53
x = 53/13
.
find y by plugging x into:
y=-3/2x +12
y=-3/2(53/13) +12
2y = -3(53/13) +24
26y = -3(53) +312
26y = -159 +312
26y = 153
y = 153/26
.
intersects at (53/13, 153/26)
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
Y=mX+b where m=slope & b= the Y intercept.
(3,4) and (11,18).
m=(Y2-Y1)/(X2-X1)
m=(18-4)/(11-3)
m=14/8=1.75 ans. for the slope
4=1.75*3+b
4=5.25+b
b=4-5.25
b=-1.25 ans. for thew Y intercept.
Y=1.75X-1.25 (red line)
------------------------------
y=-3/2x +12
Y=-3x/2+12 (green line)
(graph 300x200 pixels, x from -6 to 5, y from -10 to 15, of TWO functions 1.75x -1.25 and -3x/2 +12).
1.75x-1.25=-3x/2+12
1.75x+3x/2=12+1.25
1.75x+1.5x=13.25
3.25x=13.25
x=13.25/3.25
x=4.077 ans for the x intercept
y=1.75*4.077-1.25
y=7.135-1.25
y=5.885 ans. for the Y intercept.
(4.077,5.885) is the intercept point.
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