X and y values

Question

Find the value of x or y so that the line through the pair of points has the given slope.

 

(x,2) and (5,8); m= 1

 

step by step instruction is greatly appreciated! Thank you

Answer 1

Here's some step-by-step instructions for you:

 

So they've given you a pair of points and a slope.  Sounds like it's time to use the "rise over run" thing you've probably been hearing in your classroom.

 

Basically, "slope" is an indication of how much the x and y values of the line change from point A to point B (literally).  To do that, we have to find the difference between the start and finish x value, and the start and finish y value, by subtracting one from the other.  Now, technically, we can subtract them in either order, as long as we keep it consistent throughout the whole problem.  Generally we'd go with the second pair first, since it's often the larger number and that cuts out some unnecessary work with negatives.  So let's use the point (5,8) first and the point (x,2) second.

 

Now, that "rise over run" thing is to let you know which values go where in the problem.  "Rise" means the y-value, the one that goes up and down over time.  "Run" is the x-value, the one that runs back and forth over time.  So our problem would be:

 

slope ("m") = rise  =  (8 - 2)

                     run      (5 - x)

 

And they've told us that the slope is 1, so your equation is:

 

1  =  (8 - 2)   =     6            

        (5 - x)        5 - x

 

now multiply both sides by the quantity (5-x) to get the fraction out of there

 

5 - x  =  6                          

 

I don't like unnecessary negatives, so I'm going to do a slightly round-about move here:

 

5  =  6 + x

5 - 6  = x

so

x  = -1

 

so the x value they were asking for is -1.  Hope this cleared things up a bit!

Answer 2

 Slope between 2 given point in a rectangular coordinate system is

 

 difference between y coordinate/ difference in x coordinate

 

    Two given points  A ( X_1, Y_{1)  and} B(X₂, Y₂₎

 

    Designated by  m = (Y_{2 -} Y₁) / ( X₂ - X₁₎  ( 1)

 

  Here 2 points given are ( X, 2), and ( 5, 8)  m =1

 

  So, Using formula (1) :

     

     ( 8 - 2) / (5 -x) =1

 

    Solving for X:

 

      6/ (5-x) =1

 

     6 = 5 -x

 

     X = 5 -6 = -1

    There is no reason for not being approved

 

  Slope is given as (Y_{2 -} Y_{1)/ (} X ₂ - X₁) (1)

  Given Values of problem has been plugged in equation (1)

 and solved for the unknown which is the Y coordinate of 2nd point, and answer matches other people's answer.