<span> -6x+3y=(189/10) </span>Geometric figure: Straight Line<span> Slope = 2 x-intercept = -63/20 = -3.15000 y-intercept = 63/10 = 6.30000</span>
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "18.9" was replaced by "(189/10)".
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
-6*x+3*y-((189/10))=0
Step by step solution :<span>Step 1 :</span> 189
Simplify ———
10
<span>Equation at the end of step 1 :</span> 189
(3y - 6x) - ——— = 0
10
<span>Step 2 :</span>Rewriting the whole as an Equivalent Fraction :
<span> 2.1 </span> Subtracting a fraction from a whole
Rewrite the whole as a fraction using <span> 10 </span> as the denominator :
3y - 6x (3y - 6x) • 10
3y - 6x = ——————— = ——————————————
1 10
<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
<span>Step 3 :</span>Pulling out like terms :
<span> 3.1 </span> Pull out like factors :
3y - 6x = -3 • (2x - y)
Adding fractions that have a common denominator :
<span> 3.2 </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:
-3 • (2x-y) • 10 - (189) -60x + 30y - 189
———————————————————————— = ————————————————
10 10
<span>Step 4 :</span>Pulling out like terms :
<span> 4.1 </span> Pull out like factors :
-60x + 30y - 189 = -3 • (20x - 10y + 63)
<span>Equation at the end of step 4 :</span> -3 • (20x - 10y + 63)
————————————————————— = 0
10
<span>Step 5 :</span>When a fraction equals zero :<span><span> 5.1 </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:
-3•(20x-10y+63)
——————————————— • 10 = 0 • 10
10
Now, on the left hand side, the <span> 10 </span> cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
-3 • (20x-10y+63) = 0
Equations which are never true :
<span> 5.2 </span> Solve : -3 = 0
<span>This equation has no solution.
</span>A a non-zero constant never equals zero.
Equation of a Straight Line
<span> 5.3 </span> Solve <span> 20x-10y+63 </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> 20x-10y+63 = 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 63/10 so this line "cuts" the y axis at y= 6.30000
y-intercept = 63/10 = 6.30000 Calculate the X-Intercept :
When y = 0 the value of x is -63/20 Our line therefore "cuts" the x axis at x=-3.15000
x-intercept = -63/20 = -3.15000 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 6.300 and for x=2.000, the value of y is 10.300. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 10.300 - 6.300 = 4.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 2Geometric figure: Straight Line<span> Slope = 2 x-intercept = -63/20 = -3.15000<span> y-intercept = 63/10 = 6.30000 </span></span>
