Select the correct points. Identify the pair of points that can represent an increasing function that has a greater rate of change than that of the function
y=8/5x+3/5

Slope     =  3.200/2.000 =  1.600

Geometric figure: Straight Line

 Slope = 3.200/2.000 = 1.600

 x-intercept = 3/8 = 0.37500

 y-intercept = -3/5 = -0.6000

Step-by-step explanation:  Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    y-(8/5*x-3/5)=0

STEP

1

:

           3

Simplify   —

           5

Equation at the end of step

1

:

        8         3

 y -  ((— • x) -  —)  = 0

        5         5

STEP

2

:

           8

Simplify   —

           5

Equation at the end of step

2

:

        8         3

 y -  ((— • x) -  —)  = 0

        5         5

STEP

3

:

Adding fractions which have a common denominator :

3.1       Adding fractions which have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

8x - (3)     8x - 3

————————  =  ——————

   5           5  

Equation at the end of step

3

:

      (8x - 3)

 y -  ————————  = 0

         5    

STEP

4

:

Rewriting the whole as an Equivalent Fraction :

4.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  5  as the denominator :

         y     y • 5

    y =  —  =  —————

         1       5  

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 :

4.2       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 • 5 - ((8x-3))     5y - 8x + 3

————————————————  =  ———————————

       5                  5    

Equation at the end of step

4

:

 5y - 8x + 3

 ———————————  = 0

      5    

STEP

5

:

When a fraction equals zero :

5.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 5y-8x+3

 ——————— • 5 = 0 • 5

    5  

Now, on the left hand side, the  5  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  5y-8x+3  = 0

Equation of a Straight Line

5.2     Solve   5y-8x+3  = 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  5y-8x+3  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is -3/5 so this line "cuts" the y axis at y=-0.60000

 y-intercept = -3/5  = -0.60000

Calculate the X-Intercept :

When y = 0 the value of x is 3/8 Our line therefore "cuts" the x axis at x= 0.37500

 x-intercept = 3/8  =  0.37500

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 -0.600 and for x=2.000, the value of y is 2.600. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 2.600 - (-0.600) = 3.200 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / R

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.