Algebra Period 3 (Tuesday)

Graphing Linear Equations 7-2

How do you determine whether a given number is a solution?
.. as the commercial states... 'Plug it in, plug it in, plug it in.!'

Determine whether (3,7) is a solution of y = 2x + 1
y= 2x + 1
7 ? 2(3) + 1 substituted 3 for x and 7 for y

7 = 7 The equation is TRUE!!

Determine whether ( -2, 3) is a solution of 2y = 4x -8

2y = 4x - 8
2(3) ? 4(-2) - 8

6 ≠ 16 The equation is FALSE!!

How do you find a solution to an equation yourself?

Plug in for x and FIND y!!

Find 3 solutions of y -3x = -2

Solving for y first makes it easier to substitute for x and compute. so

change y - 3x = -2 to y = 3x - 2
We can substitute values for x and find corresponding y values.
We choose any value for x-- start with the easiest. x = 0

y = 3x - 2 substitute zero in for x

y = 3(0) - 2

y = -2 So the ordered pair (0,-2) is a solution.

Choose another number-- how about x = 2

y= 3(2) -2
y = 4 so the ordered pair ( 2, 4) is a solution

Choose another number This time let's use x = -2

y = 3(-2) - 2
y = -6 -2 which becomes y = -6 + -2
y = -8 so the ordered pair ( -2, -8) is a solution

How can you graph a linear equation? Make an x/y table of values and then graph the coordinates. You only really need 2 points-- because 2 points determine one line.
HOWEVER, always make a table of 3 ordered pairs to make sure no errors have occurred in your calculations. All 3 points will be on 1 line.

I always try to use x = 0 and solve for y and then set y = 0 and solve for x. It is usually easy. Then pick another value for x and solve for y. If this doesn't work well ( if you get a fraction as an answer-- and that isn't easy to graph) then try setting x = 1, then x = 2, then x = 3.

The graph of an equation is a drawing that represents the solution set. So 'to graph an equation' means to draw the graph of its solution set. You MUST connect the points to show the solution set. Make sure your line has arrows at both ends!!