Question

Y=x2+3x+2 y=x2+5x-4 solutions

Answer 1

Answer:

 Slope = 1

 x-intercept = 2/1 = 2.00000

 y-intercept = 2/-1 = -2.00000

Step-by-step explanation:

Pulling out like terms :

2.1     Pull out like factors :

  -2x + 2y + 4  =   -2 • (x - y - 2)

Equation at the end of step  2  :

 -2 • (x - y - 2)  = 0

Step  3  :

Equations which are never true :

3.1      Solve :    -2   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Equation of a Straight Line

3.2     Solve   x-y-2  = 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  x-y-2  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 2/-1 so this line "cuts" the y axis at y=-2.00000

 y-intercept = 2/-1  = -2.00000

Calculate the X-Intercept :

When y = 0 the value of x is 2/1 Our line therefore "cuts" the x axis at x= 2.00000

 x-intercept = 2/1  =  2.00000

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -2.000 and for x=2.000, the value of y is 0.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 0.000 - (-2.000) = 2.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

    Slope     = 1

Geometric figure: Straight Line

 Slope = 1

 x-intercept = 2/1 = 2.00000

 y-intercept = 2/-1 = -2.00000

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