on a graph... A(1,-1) and B(5,-5)  and a line goes through 0,4 and 6,0. please help solve and answer...... 1. line k has an x-intercept ___________and y-intercept ___________ 2. the slope of...

on a graph... A(1,-1) and B(5,-5)  and a line goes through 0,4 and 6,0.

please help solve and answer......

1. line k has an x-intercept ___________and y-intercept ___________

2. the slope of line k is________

3.  write the equation of line k in slope intercept form (y=mx + b)

4.  write the equation of line k in standard form (Ax + By = C)

5.  draw line AB and prove AB `_|_` k.   (an arrow going in both directions is suppose to be over both AB's) where would

this be located on the graph?

6.  on the graph draw a line j through point A, parallel to line k.  (where would this be located on the graph?)

7.  find the distance between line j and line k. 

Hint: note the coordinates where AB and line k intersect. Find the distance between points A and the point of intersection.

(an arrow goes in both directions over AB)

Thanks! 

Asked on by marley112

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steveschoen | College Teacher | (Level 1) Associate Educator

Posted on

1) (6,0), (0,4)

2) -2/3

3) y = -2/3 x + 4 is the equation for line K

4) 2x + 3y = 12

 

 

5) 

slope of this line = (-5 - -1)/(5 - 1) = -1

Perpendicular lines have slopes that are negative reciprocals.  But, here, -1 and -2/3 aren't negative reciprocals.  So, these lines aren't perpendicular.

 

 

6) 

 

 

7) The shortest distance is on the line perpendicular to these two lines.  So, that slope of this would be m = 3/2.

Now, need a point that is going to be on that line.  In analyzing the "hint", the distance between "the point of intersection of lines AB and K" and point A, that isn't the distance between lines J and K.  This information doesn't seem valuable.

We can use any point on lines K or J.  We will use point (0,4).  The equation of this line, where we will take the shortest distance, is:

y = 3/2 x + 4

We need the equation for line j.  Using m = -2/3 (parallel to line K) and A(1,-1), we get:

-1 = (-2/3)*1 + b

-1 = -2/3 + b

b = -1/3

So, the equation for line J is:

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

 

Setting the line with the shortest distance and line J equal to each other (yJ = yK), we get:

 

(3/2)x + 4 = (-2/3)x + (-1/3)

(13/6)x = -13/3

x = -2

 

Plugging this into the equation for line J, we get:

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

y = 1

 

So, we need to find the distance between (-2,1) and (0,4).  We use the distance formula for this:

d = `sqrt((-2-0)^2+(1-4)^2)`

d = `sqrt(13)`

d = 3.606

 

So, the distance between these points is 3.606 units.

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