1. y=1/2x-3
First thing to remember is the formula:
y=mx+b
m represents the slope
and b represents the y-intercept
so for the first problem m would be 1/2, which means the slope would be 1/2
y intercept for this problem would be -3
graphing first equation:
since our y intercept is -3 we would go down 3 points, so put a dot at (0,-3)
plug in 0 for y and solve
0=1/2x-3
+3 +3
3=1/2x-0
3=1/2x
multiply each side by 2
6=2 * 1/2x (we do this to get rid of the 1/2)
6=1x
divide by 1
6=x
then you can put another dot at (6,0) then draw the line
2. 3x+y=2
this equation is different because it isnt in y=mx+b form, so you have to do some algebra
3x+y=2
subtract 3x from both sides to get:
y=-3x+2
now looking back that m represents slope and b represents y intercept
slope in this case would be -3 and y intercept would be 2
graphing second equation:
since the y intercept for this problem is 2 we would go up 2 so put a dot at (0,2)
set the equation to 0 (when y is zero x is...) again find the other coordinate value:
0=-3x+2
-2 -2
-2=-3x
divide by -3
2/3=x
(two negatives make a positive)
the best way to put the dot is put it close to the half mark between one and zero
then draw the line
3. this problem is the same as the previous one but you do exactly the same thing as before
2x-y=3
-2x -2x
-y=3-2x
multiply by -1 to get rid of the negative (2 becomes positive in this case but the 3 becomes negative)
y=2x-3
slope for this problem would be 2 and the y intercept would be -3
graphing third equation:
since the y intercept is -3 we would go down 3 points, so put a dot at (0,-3)
again solve for 0 for this equation
0=2x-3
+3 +3
3=2x
divide by two on both sides
3/2=x
3/2 is same as 1.5
put the dot between 1 and 2 directly in the middle (1.5,0)
then draw the line
