Solve the following equation for y
24x - 8y = 72
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1 Answer



Step-by-step explanation:

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





Pulling out like terms

1.1     Pull out like factors :

  24x - 8y - 72  =   8 • (3x - y - 9)

Equation at the end of step






Equations which are never true:

2.1      Solve :    8   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Equation of a Straight Line

2.2     Solve   3x-y-9  = 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  3x-y-9  = 0 and calculate its properties

Graph of a Straight Line :


Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 9/-1 so this line "cuts" the y axis at y=-9.00000

 y-intercept = 9/-1  = -9.00000

Calculate the X-Intercept :

When y = 0 the value of x is 3/1 Our line therefore "cuts" the x axis at x= 3.00000

 x-intercept = 9/3  =  3

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 -9.000 and for x=2.000, the value of y 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 - (-9.000) = 6.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

    Slope     = 3

Geometric figure: Straight Line

 Slope = 3

 x-intercept = 9/3 = 3

 y-intercept = 9/-1 = -9.00000

Lilyan Larkin
15.5k 3 10 26
answered 11 months ago