<span>Equation at the end of step 1 :</span> 15
(2x - y) - ((—— • x) + 3y) = 0
4
<span>Step 2 :</span>Rewriting the whole as an Equivalent Fraction :
<span> 2.1 </span> Adding a whole to a fraction
Rewrite the whole as a fraction using <span> 4 </span> as the denominator :
3y 3y • 4
3y = —— = ——————
1 4
<span>Equivalent fraction : </span>The fraction thus generated looks different but has the same value as the whole
<span>Common denominator : </span>The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
<span> 2.2 </span> 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:
15x + 3y • 4 15x + 12y
———————————— = —————————
4 4
<span>Equation at the end of step 2 :</span> (15x + 12y)
(2x - y) - ——————————— = 0
4
<span>Step 3 :</span>Rewriting the whole as an Equivalent Fraction :
<span> 3.1 </span> Subtracting a fraction from a whole
Rewrite the whole as a fraction using <span> 4 </span> as the denominator :
2x - y (2x - y) • 4
2x - y = —————— = ————————————
1 4
<span>Step 4 :</span>Pulling out like terms :
<span> 4.1 </span> Pull out like factors :
15x + 12y = 3 • (5x + 4y)
Adding fractions that have a common denominator :
<span> 4.2 </span> Adding up the two equivalent fractions
(2x-y) • 4 - (3 • (5x+4y)) -7x - 16y
—————————————————————————— = —————————
4 4
<span>Step 5 :</span>Pulling out like terms :
<span> 5.1 </span> Pull out like factors :
-7x - 16y = -1 • (7x + 16y)
<span>Equation at the end of step 5 :</span> -7x - 16y
————————— = 0
4
<span>Step 6 :</span>When a fraction equals zero :<span><span> 6.1 </span> When a fraction equals zero ...</span>
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the <span>denominator, </span>Tiger multiplys both sides of the equation by the denominator.
Here's how:
-7x-16y
——————— • 4 = 0 • 4
4
Now, on the left hand side, the <span> 4 </span> cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
-7x-16y = 0
Equation of a Straight Line
<span> 6.2 </span> Solve <span> -7x-16y </span> = 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.
<span>In this formula :
</span><span>y </span>tells us how far up the line goes
<span>x </span>tells us how far along
<span>m </span>is the Slope or Gradient i.e. how steep the line is
<span>b </span>is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the<span> line properties.</span> We shall now graph the line <span> -7x-16y = 0</span> and calculate its properties
Graph of a Straight Line :<span>
</span>Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 0/-16 so this line "cuts" the y axis at y=-0.00000
y-intercept = 0/-16 = -0.00000 Calculate the X-Intercept :
When y = 0 the value of x is 0/-7 Our line therefore "cuts" the x axis at x=-0.00000
x-intercept = 0/-7 = -0.00000 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 0.000 and for x=2.000, the value of y is -0.875. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -0.875 - 0.000 = -0.875 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = -0.875/2.000 = -0.438 Geometric figure: Straight Line<span> Slope = -0.875/2.000 = -0.438 x-intercept = 0/-7 = -0.00000 y-intercept = 0/-16 = -0.00000
hope this helps hope i am brainliest i need one more
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