# Identify the slope and y-intercept of the linear equation 2x + 2y = 8

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2x-2y+8=6? convert the equation to slope intercept form 2y=2x+8-6 2y=2x+2 /2 y=x+1 compare with y = mx+b m= slope = 1 y intercept =b = 1

We think you wrote:

This solution deals with the properties of a straight line.

y-i"ntercept=4/-1=-4.00000

1.1     Pull out like factors :

2x - 2y - 8  =   2 • (x - y - 4)

## Step  2  :

#### Equations which are never true :

2.1      Solve :    2   =  0

This equation has no solution.
A a non-zero constant never equals zero.

#### Equation of a Straight Line

2.2     Solve   x-y-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.

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-4  = 0 and calculate its properties

#### Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 4/-1 so this line "cuts" the y axis at y=-4.00000

y-intercept = 4/-1 = -4.00000

#### Calculate the X-Intercept :

When y = 0 the value of x is 4/1 Our line therefore "cuts" the x axis at x= 4.00000

x-intercept = 4/1 = 4.00000

#### 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 -4.000 and for x=2.000, the value of y is -2.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -2.000 - (-4.000) = 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

1.   Slope = 1
2.   x-intercept = 4/1 = 4.00000
3.   y-intercept = 4/-1 = -4.00000

#### Page 2

We think you wrote:

This solution deals with the properties of a straight line.

y-i"ntercept=4/-1=-4.00000

1.1     Pull out like factors :

2x - 2y - 8  =   2 • (x - y - 4)

## Step  2  :

#### Equations which are never true :

2.1      Solve :    2   =  0

This equation has no solution.
A a non-zero constant never equals zero.

#### Equation of a Straight Line

2.2     Solve   x-y-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.

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-4  = 0 and calculate its properties

#### Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 4/-1 so this line "cuts" the y axis at y=-4.00000

y-intercept = 4/-1 = -4.00000

#### Calculate the X-Intercept :

When y = 0 the value of x is 4/1 Our line therefore "cuts" the x axis at x= 4.00000

x-intercept = 4/1 = 4.00000

#### 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 -4.000 and for x=2.000, the value of y is -2.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -2.000 - (-4.000) = 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

1.   Slope = 1
2.   x-intercept = 4/1 = 4.00000
3.   y-intercept = 4/-1 = -4.00000