SOLUTION: For my homework it says 'Find the value of x or y so that the line passing through the two points has a given slope.' For this problem, find the value of x. (x,-7), (1,2); m=3

Algebra ->  Linear-equations -> SOLUTION: For my homework it says 'Find the value of x or y so that the line passing through the two points has a given slope.' For this problem, find the value of x. (x,-7), (1,2); m=3      Log On


   

Question 1161035: For my homework it says 'Find the value of x or y so that the line passing through the two points has a given slope.'
For this problem, find the value of x.
(x,-7), (1,2); m=3
I am unsure of how to solve this, or about my answer, but I got
x=2.
Please tell me if it's correct and explain how to solve these types of problems...
Thank You!
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.

With the given coordinates, the slope is equal to

    %282-%28-7%29%29%2F%281-x%29,    or     9%2F%281-x%29 



According to the condition, the slope is 3.



It gives you THIS equation

     9%2F%281-x%29 = 3.


Cross multiply and simplify

    9 = 3*(1-x)

    9 = 3 - 3x

    3x = 3 - 9 = -6

     x         = -6%2F3 = -2.     ANSWER

Solved.

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Is everything clear to you now ?

At this site,  there is a group of lessons related to this class of problems
    - Find the slope of a straight line in a coordinate plane passing through two given points
    - Equation for a straight line having a given slope and passing through a given point
    - Solving problems related to the slope of a straight line
    - Equation for a straight line in a coordinate plane passing through two given points
    - Equation for a straight line parallel to a given line and passing through a given point
    - Equation for a straight line perpendicular to a given line and passing through a given point
    - Advanced problems on finding equations for straight lines

    - OVERVIEW of lessons related to the slope of a straight line

Consider them as your textbook,  handbook,  tutorials and  (free of charge)  home teacher.




Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


You should know how to solve problems like this using the formula for finding the slope of the line containing two given points, as shown by the other tutor.

However, beginning students especially often get wrong answers because they plug the numbers in the wrong places in the formula.

I always encourage students to learn to be able to solve this kind of problem using the basic definition of slope instead of the formula.

Slope is the ratio "rise/run" -- the ratio of how far you move up or down compared to how far you move right or left.

Between the two given points A(x,-7) and B(1,2), we don't now the run (difference in x coordinates), but we know the difference in the y coordinates from A to B is from -7 to +2, which is 9.

Since we are given that the slope is 3, we know that change of 9 in the y coordinate is 3 times the change in the x coordinate -- so the change in the x coordinate is 9/3 = 3.

B has an x coordinate of 1; the x coordinate of A has to be 3 less than that, which is 1-3 = -2.

ANSWER: x = -2