Solution - Properties of a straight line

Rearrange:

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

                     7*x-8*y-(-9)=0 

Step  1  :

Equation of a Straight Line

 1.1     Solve   7x-8y+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  7x-8y+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 9/8 so this line "cuts" the y axis at y= 1.12500

  y-intercept = 9/8  =  1.12500 

Calculate the X-Intercept :

When y = 0 the value of x is -9/7 Our line therefore "cuts" the x axis at x=-1.28571

  x-intercept = -9/7  = -1.28571 

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 1.125 and for x=2.000, the value of y is 2.875. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 2.875 - 1.125 = 1.750 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

    Slope     =  1.750/2.000 =  0.875 

Geometric figure: Straight Line

1.   Slope = 1.750/2.000 = 0.875
2.   x-intercept = -9/7 = -1.28571
3.   y-intercept = 9/8 = 1.12500