Expert: Sherry Wallin - 11/26/2008

Question
Hello homeschool parent and I don't know any of this and I have yet to receive the answer key from the curriculum please help me in answering these questions. Thanks God bless

Find the equation of the given line(in standard form)

1. The line that passes through the points (5,3) and (2,-1)
2. The line with a slope of 1/2 intersecting the y-axis at -4
3. The line with the point (-3,0) and m = 5
4. The line with the point (1,-4) and intersecting 3x + 2y = 12 at y = 3

Solve the systems of equations.
5. x - 2y = 4x + 3y =-6

Graph the following equations, inequalities, and systems. Give all the points please.
6. 4x + 3y = 12

       2
7. y = ---- x - 5
       3
  y + x=3

8. 2x - 3y > -2

9. y < 3x - 1

10. y > -4
   2x + y < 5

Answer
All lines have a slope called "m" =(y2-y1)/(x2-x1)where (x1,y1) is one of the points and (x2,y2) is another. So you need to calculate the slope and then put it into the formula * y-y1 = m(x-x1). The x and y without numbers just leave them alone in the equation. For example if I have these two points (2,1) and (-1,3) I will let x1=2 and y1=1 and x2=-1 and y2=3 so m =(3-(-1))/(-1-2)=4/-3 =-4/3 Now use either of the points given and put it into the formula * I gave you above. I will use (x1,y1) = (2,1) so y-1=(-4/3)(x-2). You can do #1 this way and for #2 you need to realize that x is always 0 on the y-axis so you have the point (0,-4)as (x1,y1) and "slope" is m. #3 "m, the slope" is already given to you so use it with the point (-3,0) given as your (x1,y1). Finding the equation in standard form is a whole other lesson. I will try to explain it to you and use my example and find the equation for it.
Standard Form means AX BY=C so you need to take the equation you get in 1,2,3 and make the coefficients (A,B,C) into integers and put the x and y terms on the left and the C on the right. By the way C is also called the constant. y-1=(-4/3)(x-2) on the right when I multiply I need to use the distributive law and that means I need to  multiply (-4/3) on the x as well as (-4/3) on the -2. So on the right we have (-4/3)x  8/3. On the left we still have y -1 so add the 1 so you get y by itself. Notice also that the coefficient B is 1 on Y already so you needn't make any changes for it. But on the right you now have (-4/3)x  11/3. Notice they both have a 3 in the denominator and you can multiply both sides by 3 to make the numbers on the right integers getting 3y = -4x   11 and finally add 4x to both sides and get 4x 3y=11 which is in standard form.
For #4 they give you the y=3 to put into the equation to solve for x of the "other" point (x,3)so that you can use the two points to find the slope and then use one of the points with the slope to find the equation.

I am willing to answer some of these other questions but first you need to see if you can follow what I have done and if you need more assistance please write again. I would like to see what answers you come up with so that I know you understand. The next requires a higher level of thinking.

Have a Happy Turkey Day,
Math Prof