Probability & Statistics

Question

Find the slope and the y-intercept for the line that passes through (-6,1) (4,2)

The slope is=
 

The y-intercept is =


d. Find the slope and the y-intercept for the line that passes through (-8,-4) (7,6)

The slope is =


The y-intercept is =

 

 

****please show workup and answers should be shown as a fraction

Answer 1

Hi Mik;

FIRST QUESTION...

slope=m=(y-y₁)/(x-x₁)

 

m=(1-2)/(-6-4)=-1/-10=1/10

The slope-intercept formula is...

y=mx+b

y=(1/10)x+b

Let's plug-in one coordinate...

1=(1/10)(-6)+b

1=(-6/10)+b

Let's add 6/10 to both sides...

1+(6/10)=(-6/10)+b+(6/10)

1 6/10=b

1 3/5=b

The formula is...

y=(1/10)x+(1 3/5)

Let's plug-in the other coordinate to see verify the results...

y=(1/10)x+b

2=(1/10)(4)+b

2=(2/5)+b

Let's subtract 2/5 from both sides...

2-(2/5)=(2/5)+b-(2/5)

1 3/5=b

y=(1/10)x+(1 3/5)

Same results!

slope is 1/10

y-intercept, value of y when x=0, is 1 3/5

 

SECOND QUESTION...

slope=m=(y-y₁)/(x-x₁)

m=(-4-6)/(-8-7)

m=-10/-15=2/3

y=mx+b

y=(2/3)x+b

Let's plug-in one coordinate...

-4=(2/3)(-8)+b

-4=(-16/3)+b

For convenience, let's convert the 4 into 3rds...

-12/3=(-16/3)+b

Let's add (16/3) to both sides...

(16/3)-(12/3)=(-16/3)+b+(16/3)

4/3=b

1 1/3=b

y=(2/3)x+ 1 1/3

Other coordinate...

6=(2/3)(7)+ b

6=(14/3)+b

18/3=(14/3)+b

4/3=b

1 1/3=b

y=(2/3)x+ 1 1/3

Results are identical!

Slope is 2/3.

y-intercept, value of y when x=0, is 1 1/3.

Answer 2

First for question 1.

Find the slope and the y-intercept for the line that passes through (-6,1) (4,2)

 

Remember that slope follows the saying "rise over run"

what that really means is "what is the difference in y" over "the differences in x"

so lets call (-6,1) point A

and lets call (4,2) point B

 

well A-B (y values) over A-B (x values) and that gives you your slope (after simplification of course)

 

to obtain a y intercept one way is to just build a slope intercept form equation 

y=mx+b

 

to do that start with point slope form (for the sake of argument we will use point A only)

point slope form starts off as y-(y value for point A)= (slope)(x-(x value for point A))

solve for y and your constant value (the one without a variable) is your y intercept

 

Have fun