Expert: Richard J. Raridon - 3/23/2006

Question
I have a couple questions for you again..... sorry I am really trying....

1) Find the slope that passes through (4,-8) and (1,4).

2) Explain why (-3,2) is not on the same line as (4,-8) and (1,4).

3) What is the slope of the line 5x+3y=4?

4)Write an equation in slope-intercept form for the line with slope -4 and y-intercept -6.

5)Write an equation in slope-intercept form for the line with x-intercept 5 and y-intercept -3.

6)Give an equation for the line with slope -1 and y-intercept 3.

7)Write an equation for the line through (2,4) and (-1,5).

8)Write an equation for the line through (-5,3) and (2,4).

9)Write an equation for the line through (7,-1) and (0,-4).

10) What is the slope of a line that passes through (7,1) and (0,-4)?

11) Find the slope and the y-intercept of the line 3x-y=9.

12) Find the slope and the y-intercept of the line 2x-3y=5.

13) Find the slope and the y-intercept of the line y=-5+2/3x.

14) Find the slope and y-intercept of the line y=-8+2/5x.

15) Rewrite the equation y=3x+2 in standard form.

16) Rewrite the equation y=-3/10x+2 in standard form.

17) Write the equation 2x+3y=3 in slope intercept form.

18) T or F.....every vertical line has no slope.

19) Do the points (1,7), (-2,-2), and (0,4) lie on the same line.....explain.

20) Graph the line with slope 1 that passes through (3,1)and then write an equation for the line.

21) Graph the inequality y<-x+3.

22) Graph the inequality 2y+-3x_<4.

23) Graph the inequality y_<-2x-4.  

Answer
Most of these are variations of the same thing.  The standard equation for a line is y=mx+b where m is the slope and b is the y-intercept.  
1) Put those two points into the std. eq. and you have
-8 =4m+b and 4 =m+b so you can solve to get m=-4, b=8.
2) That point doesn't satisfy the equation y = -4x+8
3) re-write it as y = (-5/3)x +4/3 and compare it to the std. eq.
4) y = -4x-6, are you catching on?
5) two points on the line are (5,0) and (0,3).  do like 1)
6) like 4)
7) 4 =2m+b and 5 =-m+b, solve for m and b
8) same as 7)
9) same as 7)
10) same as 1)
11) re-write it as y = 3x-9 and compare with std. eq.
12) same as 11)
13) compare it to std. eq.
14) same as 13)
15 and 16) already in std. form
17) like 11)
18) or you can say the slope is infinite
19) find the eq. through the 1st two points and then find the eq. through the last two points.  If the eqs. are the same, all three points are on the same line.
20) you can graph it.  it only takes two points to draw a straight line.  if the slope is 1, then add 1 to x, 1 to y and you have a new point (4,2). now do like 7)
21) you can graph the line y = -x+3 by putting in two values for x, finding two values for y and drawing the line.  the inequality is every value below that line.  
22) re-write it 2y < 3x+4. plot 2y = 3x+4 and the inequality is every value below that line.
23) plot the line y = -2x-4 and the inequality is every value below that line.