271,955 views
5 votes
5 votes
A soup recipe requires 6 ounces of bouillon plus 2 ounces for each quart of water used.

This relationship is represented by the equation b = 2q +6, where b represents the
number of ounces of bouillon and q represents the number of quarts of water

User ElGeekalpha
by
2.7k points

1 Answer

16 votes
16 votes

Answer:

Slope=1.000/2.000=0.500

b-i

q-i

b-(2*q+6)=0

Explanation:

1.1 Solve b-2q-6 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line b-2q-6 = 0 and calculate its properties

Notice that when b = 0 the value of q is 3/-1 so this line "cuts" the q axis at q=-3.00000

q-intercept = 6/-2 = 3/-1 = -3.00000

When q = 0 the value of b is 6/1 Our line therefore "cuts" the b axis at b= 6.00000

b-intercept = 6/1 = 6.00000

Slope is defined as the change in q divided by the change in b. We note that for b=0, the value of q is -3.000 and for b=2.000, the value of q is -2.000. So, for a change of 2.000 in b (The change in b is sometimes referred to as "RUN") we get a change of -2.000 - (-3.000) = 1.000 in q. (The change in q is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = 1.000/2.000 = 0.500

Slope = 1.000/2.000 = 0.500

b-intercept = 6/1 = 6.00000

q-intercept = 6/-2 = 3/-1 = -3.00000

User Pius
by
2.6k points