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## The slope and the y-intercept

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 =

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)

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)
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.