Slope = 1.000/2.000 = 0.500
x-intercept = 16/1 = 16.00000
y-intercept = 16/-2 = 8/-1 = -8.00000
Step-by-step explanation:
Step 1 :
Equation at the end of step 1 :
((2 • (x - 2)) • 2) - 8 • (y + 7) = 0
Step 2 :
Equation at the end of step 2 :
(2 • (x - 2) • 2) - 8 • (y + 7) = 0
Step 3 :
Equation at the end of step 3 :
4 • (x - 2) - 8 • (y + 7) = 0
Step 4 :
Step 5 :
Pulling out like terms :
5.1 Pull out like factors :
4x - 8y - 64 = 4 • (x - 2y - 16)
Equation at the end of step 5 :
4 • (x - 2y - 16) = 0
Step 6 :
Equations which are never true :
6.1 Solve : 4 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Equation of a Straight Line
6.2 Solve x-2y-16 = 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-2y-16 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 8/-1 so this line "cuts" the y axis at y=-8.00000
y-intercept = 16/-2 = 8/-1 = -8.00000
Calculate the X-Intercept :
When y = 0 the value of x is 16/1 Our line therefore "cuts" the x axis at x=16.00000
x-intercept = 16/1 = 16.00000
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 -8.000 and for x=2.000, the value of y is -7.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -7.000 - (-8.000) = 1.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 1.000/2.000 = 0.500
Geometric figure: Straight Line
Slope = 1.000/2.000 = 0.500
x-intercept = 16/1 = 16.00000
y-intercept = 16/-2 = 8/-1 = -8.00000
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