Solve Propertiesstraightline G(3b)=(3b)^2-3b Tiger Algebra Solver

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : g*(3*b)-((3*b)^2-3*b)=0

Step 1 :

Equation at the end of step 1 :

Step 2 :

Step 3 :

Pulling out like terms :

3.1 Pull out like factors : 3gb - 9b2 + 3b = 3b • (g - 3b + 1)

Equation at the end of step 3 :

Step 4 :

Theory - Roots of a product :

4.1 A product of several terms equals zero.When a product of two or more terms equals zero, then at least one of the terms must be zero.We shall now solve each term = 0 separatelyIn other words, we are going to solve as many equations as there are terms in the productAny solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

4.2 Solve : 3b = 0Divide both sides of the equation by 3: b = 0

Equation of a Straight Line

4.3 Solve g-3b+1 = 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 goesx tells us how far alongm is the Slope or Gradient i.e. how steep the line isb is the Y-intercept i.e. where the line crosses the Y axisThe X and Y intercepts and the Slope are called the line properties. We shall now graph the line g-3b+1 = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when g = 0 the value of b is 1/3 so this line "cuts" the b axis at b= 0.33333

Calculate the X-Intercept :

When b = 0 the value of g is -1/1 Our line therefore "cuts" the g axis at g=-1.00000

Calculate the Slope :

Slope is defined as the change in b divided by the change in g. We note that for g=0, the value of b is 0.333 and for g=2.000, the value of b is 1.000. So, for a change of 2.000 in g (The change in g is sometimes referred to as "RUN") we get a change of 1.000 - 0.333 = 0.667 in b. (The change in b is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Geometric figure: Straight Line

1. Slope = 0.667/2.000 = 0.333
2. g-intercept = -1/1 = -1.00000
3. b-intercept = 1/3 = 0.33333
4. b = 0