Solve the equation for y
y-4=1/2(x-8)

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)

true

step-by-step explanation:

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204