Determine whether y varies directly with x. If so, find the constant of variation k write the equation

It varies directly

k =

Step-by-step explanation:

Table:

    x      y

   7       11

   8       13

   9       15

   10      17

Problem:, determine if y varies directly as x

Solution:

  The equation to determine if they vary directly is;

         y ∝  x

         y  = kx

From the table, y varies directly as x. As y increases, x also increases.

To find k, use any convenient value of y and x  ;

     y  = 15 and x  = 9;

        15 = k x 9

        k =  =

The required equation is:

Step-by-step explanation:

The slope-intercept form of a line is given by:

For writing equation of a line, slope and a point is needed from which the line passes.

In order to find the slope of line perpendicular to PQ, we have to find slope of PQ first.

Slope is denoted by m and given by the formula

Given points are:

P(-1, -4) and Q (7, 1)

Putting the values

The product of slope of two pependicular lines is -1

Let m1 be the slope of line perpendicular to PQ

Now for the point, we have to find the point that divides PQ in ratio 3:2

The formula is:

Here

m = 3

n= 2

Putting the values

So we have to write equation of a line with slope -8/5 and passing through point (19/5, -1)

Putting the values in slope-intercept form

Putting the point in the equation

Putting the value of b

Hence,

The required equation is: