The slope and the y-intercept

Question

Find the slope and the y-intercept for the line that passes through (-8,2) (11,4)

The slope is=
 

The y-intercept is =


d. Find the slope and the y-intercept for the line that passes through (-8,-11) (4,6)

The slope is =


The y-intercept is =

Answer 1

Hi Mik;

Find the slope and the y-intercept for the line that passes through (-8,2) (11,4)

The slope is the change-of-y divided by the change-of-x, also known as rise-over-run...

m=(y-y₁)/(x-x₁)

m=(2-4)/(-8-11)

m=(-2)/(-19)

m=2/19

The slope-intercept formula is...

y=mx+b

b is the y-intercept, the value of y when x=0.

y=(2/19)x+b

Let's plug-in one set of coordinates...

2=(2/19)(-8)+b

2=-16/19+b

Let's add 16/19 to both sides of the equation...

(16/19)+2=(-16/19)+b+(16/19)

2 16/19=b

y=(2/19)x+(2 16/19)

Let's check our results with the other set of coordinates...

y=(2/19)x+b

4=(2/19)(11)+b

4=(22/19)+b

4=(1 3/19) +b

Let's subtract 1 3/19 from both sides...

2 16/19=b

y=(2/19)x+(2 16/19)

 

d. Find the slope and the y-intercept for the line that passes through (-8,-11) (4,6)

m=(y-y₁)/(x-x₁)

m=(-11-6)/(-8-4)

m=(-17)/(-12)

m=(17)/(12)

m=1 5/12

m=(1 5/12)x+b

m=(17/12)x+b

Let's plug-in one set of coordinates to establish b, the y-intercept.

y=mx+b

-11=(17/12)(-8)+b

-11=-(136/12)+b

-11=-(11 4/12)+b

-11=(-11 1/3)+b

Let's add 11 1/3 to both sides...

1/3=b

y=(1 5/12)x+(1/3)

Other coordinates...

y=mx+b

y=(1 5/12)x+b

6=(1 5/12)(4)+b

6=(17/12)(4)+b

6=(68/12)+b

6=(34/6)+b

6=(17/3)+b

6=(5 2/3)+b

1/3=b

y=(1 5/12)x+(1/3)

 

Answer 2

points (-8,2) and (11,4)

y=mx+b

slope= rise/run

slope=(4-2)/[11-(-8)]

slope=2/19

y=(2/19)x+b

y-y1=m(x-x1) is called the point-slope form of the equation of the line

using either point:

y-4=(2/19)(x-11)

y-4=(2/19)x-(22/19)

y=(2/19)x+4-(22/19)

y=(2/19)x+(54/19)

or

y-2=(2/19)(x+8)

y=(2/19)x+(16/19)+2

y=(2/19)x+(54/19)

slope=(2/19) and y-intercept=(54/19)

Answer 3

Points ( -8, 2) , ( 11, 4)

 

 

  Another Merthod will be:

 

     2 = -8m +b

     4 = 11m + b

 

    Solving this system of equation:

 

      Subtracting first from the second:

 

     2 = 19 m     m= 2/19

 

    Substitution in 2nd equation:

      4 = 11( 2/19) +b

 

        b = 76/19- 22/19 = 54/19

 

         Y = 2/19 X + 54/19

 

       The important thing is to realize that all these methods stem from the same principle, and diversity in

       

          math gives  us a chance to use every one of these features in more advanced courses.