What is the equation of the line that passes through the point (-8, 3) and has a
slope of -1/4

Given parameters:

 Slope of the line  =

 Coordinates of the points = (-8, 3)

Unknown:

Equation of the line = ?

Solution:

To find the equation of the line, we must note that any straight line can be represented by the equation;

        y  = mx + c

 where x and y are the coordinates

             m is the slope

              c is the y-intercept of the line

Input the parameters and solve for c;

     x = -8 and y  = 3;

         3  = x (-8) + c

         3 = 2 + c

        c  = 1;

  So the equation of the line is ;

     y  = x + 1

     multiply through by 4;

   4y = -x + 4

The equation of the line is 4y = -x + 4

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."

include a picture of the drawing in order for me to

step-by-step explanation: