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+11^2+y+4^2-(289)=0
Step 1 :
1.1 4 = 22
(4)2 = (22)2 = 24
Equation at the end of step 1 :
(((x + (112)) + y) + 24) - 289 = 0
Step 2 :
Equation at the end of step 2 :
(((x + 112) + y) + 24) - 289 = 0
Step 3 :
Equation at the end of step 3 :
x + y - 152 = 0
Step 4 :
Equation of a Straight Line
4.1 Solve x+y-152 = 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-152 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 152/1 so this line "cuts" the y axis at y=152.00000
y-intercept = 152/1 = 152.00000 Calculate the X-Intercept :
When y = 0 the value of x is 152/1 Our line therefore "cuts" the x axis at x=152.00000
x-intercept = 152/1 = 152.00000 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 152.000 and for x=2.000, the value of y is 150.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 150.000 - 152.000 = -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 = 152/1 = 152.00000
- y-intercept = 152/1 = 152.00000
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