SOLUTION: a straight line passes through (1,2) and (-3,8). find the point on it that has an x-coordinate of 5. with full details please thanks

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Question 186626This question is from textbook mathematical analysis
: a straight line passes through (1,2) and (-3,8). find the point on it that has an x-coordinate of 5.
with full details please
thanks This question is from textbook mathematical analysis

Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
First, find the eqaution of the line defined by the two given points
Solved by pluggable solver: FIND EQUATION of straight line given 2 points
hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (1, 2) and (x2, y2) = (-3, 8).
Slope a is a+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%288-2%29%2F%28-3-1%29+=+-1.5.
Intercept is found from equation a%2Ax%5B1%5D%2Bb+=+y%5B1%5D, or -1.5%2A1+%2Bb+=+3.5. From that,
intercept b is b=y%5B1%5D-a%2Ax%5B1%5D, or b=2--1.5%2A1+=+3.5.

y=(-1.5)x + (3.5)

Your graph:




Now that that equation, plug in x=5 and solve for y
y=%28-1.5%29x+%2B+%283.5%29
y=%28-1.5%295+%2B+%283.5%29
y+=+-7.5+%2B+3.5
y+=+-4
Look at the line, is the point (5,-4) on it?