Answer:
1. Slope = -4.000/2.000 = -2.000
x-intercept = 8/2 = 4
y-intercept = 8/1 = 8.00000
2. Slope = 5.000/2.000 = 2.500
x-intercept = 38/5 = 7.60000
y-intercept = 38/-2 = 19/-1 = -19.00000
Step-by-step explanation:
1.
Step 1 :
Pulling out like terms :
1.1 Pull out like factors :
4x + 2y - 16 = 2 • (2x + y - 8)
Equation at the end of step 1 :
Step 2 :
Equations which are never true :
2.1 Solve : 2 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Equation of a Straight Line
2.2 Solve 2x+y-8 = 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 2x+y-8 = 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 = 8/1 = 8.00000
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 = 8/2 = 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 8.000 and for x=2.000, the value of y is 4.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 4.000 - 8.000 = -4.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = -4.000/2.000 = -2.000
Geometric figure: Straight Line
Slope = -4.000/2.000 = -2.000
x-intercept = 8/2 = 4
y-intercept = 8/1 = 8.00000
Processing ends successfully
2.
Step 1 :
Equation of a Straight Line
1.1 Solve 5x-2y-38 = 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 5x-2y-38 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 19/-1 so this line "cuts" the y axis at y=-19.00000
y-intercept = 38/-2 = 19/-1 = -19.00000
Calculate the X-Intercept :
When y = 0 the value of x is 38/5 Our line therefore "cuts" the x axis at x= 7.60000
x-intercept = 38/5 = 7.60000
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 -19.000 and for x=2.000, the value of y is -14.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -14.000 - (-19.000) = 5.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 5.000/2.000 = 2.500
Geometric figure: Straight Line
Slope = 5.000/2.000 = 2.500
x-intercept = 38/5 = 7.60000
y-intercept = 38/-2 = 19/-1 = -19.00000
Processing ends successfully
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