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write each equation
7. x + y = 6

x+y=-6  

geometric figure: straight line

  slope = -2.000/2.000 = -1.000

  x-intercept = -6/1 = -6.

  y-intercept = -6/1 = -6.

rearrange:

rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    x+)=0  

step by step solution :

step   1   :

equation of a straight line

1.1     solve   x+y+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   x+y+6   = 0 and calculate its properties

graph of a straight line :

calculate the y-intercept :

notice that when x = 0 the value of y is -6/1 so this line "cuts" the y axis at y=-6.

  y-intercept = -6/1   = -6.  

calculate the x-intercept :

when y = 0 the value of x is -6/1 our line therefore "cuts" the x axis at x=-6.

  x-intercept = -6/1   = -6.  

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 -6.000 and for x=2.000, the value of y is -8.000. so, for a change of 2.000 in x (the change in x is sometimes referred to as "run") we get a change of -8.000 - (-6.000) = -2.000 in y. (the change in y is sometimes referred to as "rise" and the slope is m = rise / run)

    slope     = -2.000/2.000 = -1.000  

geometric figure: straight line

  slope = -2.000/2.000 = -1.000

  x-intercept = -6/1 = -6.

  y-intercept = -6/1 = -6.

nothjing

step-by-step explanation:

step-by-step explanation:

f(x)=2x^2 -1 

translation is a function transformation that transform the function in a way of translating. by translating the function its graph is moved  up an down. moving the function f(x) 2 units to the left will be the new function g(x) with the equation: g(x)=f(x+2)=2(x+2)^2 -1