SOLUTION: Problem For the points ( [3] , [6] ) and (1, [7] ), find a) the distance between the points, b) and the equation of the line passing through them. Round all numbers to 1

Algebra ->  Linear-equations -> SOLUTION: Problem For the points ( [3] , [6] ) and (1, [7] ), find a) the distance between the points, b) and the equation of the line passing through them. Round all numbers to 1       Log On


   

Question 940121: Problem
For the points ( [3] , [6] ) and (1, [7] ), find
a) the distance between the points,
b) and the equation of the line passing through them.
Round all numbers to 1 decimal place and write your answer in slope-intercept form (y = mx + b).
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given:
the points ( 3 , 6 ) and (1, 7 ),
find:
a) the distance between the points,
Solved by pluggable solver: Distance Formula to determine length on coordinate plane
The distance (d) between two points is given by the following formula:

d=sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29

Thus in our case, the required distance is
d=sqrt%28%281-3%29%5E2+%2B+%287-6%29%5E2%29=+2.23606797749979+


For more on this concept, refer to Distance formula.


so, distance is highlight%28d=2.2%29

b) and the equation of the line passing through them.
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) = (3, 6) and (x2, y2) = (1, 7).
Slope a is a+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%287-6%29%2F%281-3%29+=+-0.5.
Intercept is found from equation a%2Ax%5B1%5D%2Bb+=+y%5B1%5D, or -0.5%2A3+%2Bb+=+7.5. From that,
intercept b is b=y%5B1%5D-a%2Ax%5B1%5D, or b=6--0.5%2A3+=+7.5.

y=(-0.5)x + (7.5)

Your graph:




in slope-intercept form (y+=+mx+%2B+b):
highlight%28y=-0.5x+%2B+7.5%29