Solve Propertiesstraightline G(x)=x^2-5x 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*(x)-(x^2-5*x)=0

Step 1 :

Step 2 :

Pulling out like terms :

2.1 Pull out like factors : gx - x2 + 5x = x • (g - x + 5)

Equation at the end of step 2 :

Step 3 :

Theory - Roots of a product :

3.1 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 :

3.2 Solve : x = 0 Solution is x = 0

Equation of a Straight Line

3.3 Solve g-x+5 = 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-x+5 = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of g is -5/1 so this line "cuts" the g axis at g=-5.00000

Calculate the X-Intercept :

When g = 0 the value of x is 5/1 Our line therefore "cuts" the x axis at x= 5.00000

Calculate the Slope :

Slope is defined as the change in g divided by the change in x. We note that for x=0, the value of g is -5.000 and for x=2.000, the value of g is -3.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -3.000 - (-5.000) = 2.000 in g. (The change in g is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Geometric figure: Straight Line

1. Slope = 2.000/2.000 = 1.000
2. x-intercept = 5/1 = 5.00000
3. g-intercept = -5/1 = -5.00000
4. x = 0