Here's how:
2y+x-16
——————— • 2 = 0 • 2
2
Now, on the left hand side, the 2 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
2y+x-16 = 0
Equation of a Straight Line
4.2 Solve 2y+x-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 2y+x-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
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
Geometric figure: Straight Line
Slope = -1.000/2.000 = -0.500
x-intercept = 16/1 = 16.00000
y-intercept = 16/2 = 8
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
y-4-(-1/2*(x-8))=0
Step by step solution :
Step 1 :
1
Simplify —
2
Equation at the end of step 1 :
1
(y - 4) - (0 - (— • (x - 8))) = 0
2
Step 2 :
Equation at the end of step 2 :
(x - 8)
(y - 4) - (0 - ———————) = 0
2
Step 3 :
Rewriting the whole as an Equivalent Fraction :
3.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 2 as the denominator :
y - 4 (y - 4) • 2
y - 4 = ————— = ———————————
1 2
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
3.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
(y-4) • 2 - ((8-x)) 2y + x - 16
——————————————————— = ———————————
2y + x - 16
——————————— = 0
2
Step 4 :
When a fraction equals zero :
4.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero
Here's how:
2y+x-16
——————— • 2 = 0 • 2
2
Now, on the left hand side, the 2 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
2y+x-16 = 0
Equation of a Straight Line
4.2 Solve 2y+x-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
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 2y+x-16 = 0 and calculate its properties
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
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)
