Solution - Properties of a straight line
Step by Step Solution
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
x+6^2+y+7^2-(4)=0
Step 1 :
Equation at the end of step 1 :
(((x + (62)) + y) + 72) - 4 = 0
Step 2 :
2.1 6 = 2•3
(6)2 = (2•3)2 = 22 • 32
Equation at the end of step 2 :
(((x + (22•32)) + y) + 72) - 4 = 0
Step 3 :
Equation at the end of step 3 :
x + y + 81 = 0
Step 4 :
Equation of a Straight Line
4.1 Solve x+y+81 = 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+y+81 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is -81/1 so this line "cuts" the y axis at y=-81.00000
y-intercept = -81/1 = -81.00000 Calculate the X-Intercept :
When y = 0 the value of x is -81/1 Our line therefore "cuts" the x axis at x=-81.00000
x-intercept = -81/1 = -81.00000 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 -81.000 and for x=2.000, the value of y is -83.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -83.000 - (-81.000) = -2.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = -2.000/2.000 = -1.000 Geometric figure: Straight Line
- Slope = -2.000/2.000 = -1.000
- x-intercept = -81/1 = -81.00000
- y-intercept = -81/1 = -81.00000
How did we do?
Please leave us feedback.