Answer:
use 2 defined points.
Lets use: (-3,0) and (0,3)
The equation is written as y = mx+b, where m is the slope and is the y-intercept
Slope - change in y / change in x:
Slope = (3 -0) /(0- -3) = 3/3 = 1
b is the y-intercept which is the y value when x is o, which is one of the points (0,3) so b = 3
The equation becomes y = x +3
If lines are paralel, then they have the same slope
if the lines are pependicuilar, the slopes mutiply to -1
so
y=mx+b
m=slope
and
ax+by=c
-a/b is the slope
given
y=2/3x-2
slope is 2/3
x+y=4
slope is -1/1 or -1
2/3≠-1 and -1 times 2/3≠-1 so they are neither perpendicular or paralell
since they aren't paralell, we know they intersect somewhere
We can use the distributive property to set up an expression that is equal to this problem.
14 times 8 is 112
14 times -6 is -84x
14 times 12 is 168
(If you don't know the distributive property ask and I can explain it)
We can combine that together to get:
112 +168 -84x
Or, condense it further:
280-84x is equivalent to 14(8-6x+12)
For this case, the first thing we must do is define variables:
x: number of quarters
y: number of nickels
We now write the system of equations:
x + y = 68
0.25x + 0.05y = 13.40
Solving the system we have:
x = 50
y = 18
Answer:
they have:
quarters = 50
nickels = 18
