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NeX [460]
3 years ago
6

What are the x and y-intercepts of the line described by the equation? −6x+3y=18.9

Mathematics
1 answer:
belka [17]3 years ago
5 0
<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>
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