Find the x- and y-intercepts of the graph of the linear equation -x+8y=4

Step by step solution :

Step  1  :

Pulling out like terms :

1.1     Pull out like factors :

  -x + 8y - 4  =   -1 • (x - 8y + 4)

Equation at the end of step  1  :

Step  2  :

Equation of a Straight Line

2.1     Solve   -x+8y-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 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+8y-4  = 0 and calculate its properties.

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 1/2 so this line "cuts" the y axis at y= 0.50000

 y-intercept = 4/8 = 1/2  =  0.50000

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 0.500 and for x=2.000, the value of y is 0.750. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 0.750 - 0.500 = 0.250 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     =  0.250/2.000 =  0.125

Geometric figure: Straight Line

     Slope = 0.250/2.000 = 0.125

     x-intercept = 4/-1 = -4.00000

     y-intercept = 4/8 = 1/2 =.50000

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step-by-step explanation:

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step-by-step explanation: