Search 72,378 tutors
FIND TUTORS
Search for tutors
Ask a question
0 0

Slope and Y-intercept

Find the slope and the y-intercept for the line that passes through (-11,1) (7,8)

The slope is=
 

The y-intercept is =


d. Find the slope and the y-intercept for the line that passes through (-12,-2) (11,5)

The slope is =


The y-intercept is =


 
 
****please show workup and answers should be shown as a fraction
Tutors, please sign in to answer this question.

2 Answers

The definition of the slope of a line through points (x1, y1) and (x2, y2) is:
y2 - y1
x2 - x1
In the first case, this would be:
   8 - 1  7
7 - (-11)   18
In the second case, this would be:
  5 - (-2) 7
11 - (-12)   23
 
The y-intercept of the aforementioned line must be found by first finding the equation for the line, using the slope-intercept form y = mx + b (where m is the slope and b is the y-intercept). We have already found the slope, so we can put this in as m. We have two choices of (x, y) pairs for each case, so we can plug one of these into the equation, leaving just one unknown, b. Solve for b, and you have the y-intercept. I will do this for the first case.
 
y = 7 x + b
     18
8 = 7 (7) + b
     18
8 = 49 + b
      18
14449 = b
 18    18
b = 95
      18
 
The method for the second case is exactly the same, just with different numbers. Now you know how to find slopes and intercepts, which means you know how to write the equation of a line through two points!
 Slope by definition: / ( Y2 - Y1)           
                                ( X2 - X1)
 
    In this case will be:
                                   8 - 1       = 7  
                                   7-(-11)      18
 
  The line is a location of all points with equal slope.
 
        ( 7, 8 )    ( 0 , b), Y intercept
 
            8 - b =
             7 - 0   18
 
            144 - 18b = 49
             
               95  = 18b
                 
                b = 95   / Y intercept
                      18
    Equation of the line:
 
        Y = 7 X + b
              18
        
           8 = (7 ) + b
                 18
 
            144 = 49 + 18b
 
                  b = 95/18
 
          Y = 7/18 X + 95/18        / Y intercept = 95/18