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source : tiger-algebra.com

## Step  1  :

Pulling out like terms :

1.1     Pull out like factors :

ak – 4a – 9ab  =   a • (k – 9b – 4)

Equation at the end of step  1  :

## Step  2  :

Theory – Roots of a product :

2.1    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 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

2.2      Solve  :    a = 0

Solution is  a = 0

Equation of a Straight Line

2.3     Solve   k-9b-4  = 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 axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  k-9b-4  = 0 and calculate its properties

Graph of a Straight Line : Calculate the Y-Intercept :

Notice that when a = 0 the value of k is 4/-9 so this line “cuts” the k axis at k=-0.44444

k-intercept = 4/-9 = -0.44444 Calculate the X-Intercept :

When k = 0 the value of a is 4/1 Our line therefore “cuts” the a axis at a= 4.00000

a-intercept = 4/1 = 4.00000 Calculate the Slope :

Slope is defined as the change in k divided by the change in a. We note that for a=0, the value of k is -0.444 and for a=2.000, the value of k is -0.222. So, for a change of 2.000 in a (The change in a is sometimes referred to as “RUN”) we get a change of -0.222 – (-0.444) = 0.222 in k. (The change in k is sometimes referred to as “RISE” and the Slope is m = RISE / RUN)

Slope = 0.222/2.000 = 0.111

## Geometric figure: Straight Line

Slope = 0.222/2.000 = 0.111   a-intercept = 4/1 = 4.00000   k-intercept = 4/-9 = -0.44444  a = 0

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Solve in positive integers the equation \$a^3+b^3=9ab – Solve the equation for a. K = 4a + 9ab. Given equation is K = 4a + 9ab. Now we solve for 'a'. We need to get 'a' alone. We factor out 'a' from the right hand side. K = 4a + 9ab. K = a (4+9b) Now we divide the equation both sides by 4+9b. SoSolve the equation for a. K = 4a + 9ab . answer. a=k/4+9b. question. Anastasia uses the equation p = 0.7(rh + b) to estimate the amount of take-home pay, p, for h hours worked at a rate of r dollars per hour and any bonus received, b. What is an equivalent equation solved for h? answer.There are a couple of ways to solve this problem: First, this equation is (or is nearly) in standard form. And there is a formula for the slope of an equation in standard form: . Since the slope, m, is 3 and A = 4 and B = -k, this formula for this equation is We can solve this for k. Multiply both sides by k: Divide both sides by 3: Solve for y