3x-5y=12 Geometric figure: Straight Line Slope = 1.200/2.000 = 0.600 x-intercept = 12/3 = 4 y-intercept = 12/-5 = -2.40000 Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
3*x-5*y-(12)=0
Step 1 :Equation of a Straight Line 1.1 Solve 3x-5y-12 = 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-5y-12 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 12/-5 so this line "cuts" the y axis at y=-2.40000
y-intercept = 12/-5 = -2.40000 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 = 12/3 = 4 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 -2.400 and for x=2.000, the value of y is -1.200. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -1.200 - (-2.400) = 1.200 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 1.200/2.000 = 0.600
Geometric figure: Straight Line Slope = 1.200/2.000 = 0.600 x-intercept = 12/3 = 4 y-intercept = 12/-5 = -2.40000
