Precalc questions

Question

1. In the equation of a line, y=4x-3, the number -3 represents the________.

 

2. In the equation y=mx+b, the letter_________ represents the slope and the letter ________ represents the y- intercept. 

 

3. Points M(2,-8) and N(0,-4) are on a line. The slope of the line is _______ and the y- intercept is _________.  The equation of the line is _______.

Answer 1

The slope-intercept form for the equation of a straight line is:

 

y = mx + b

 

where m is the slope and b is the y-intercept.

 

1.  y = 4x - 3 = 4x + (-3).  -3 is the y-intercept

 

2.  y = mx + b.  m is the slope, and b is the y-intercept,

 

3.  The slope (m) of the line is the change in y over the change in x between any two points on the line.  We have two points in ordered pair format (x,y): (2,-8) and (0.-4)

 

Change in y = -4 - (-8) = -4 + 8 = 4

Change in x =  0 - 2 = -2

 

m = Change in y/Change in x = 4/(-2) = -2

 

So far:

 

y = -2x + b

 

To find b, plug one of the (x,y) points into the equation, say point M, (2,-8):

 y = -2x + b

-8 = -2(2) + b                          [Plug in y=-8, x=2]

-8 = -4 + b

-4 = b (the y-intercept)

 

The equation of the line is:

 

y = -2x -4