For the straight line defined by the points (2,55) and (4,87), determine the slope (m) and y-intercept (b). do not round the answers.

Step-by-step explanation:

It is useful to start with the 2-point form of the equation for a line. For points (x1, y1) and (x2, y2), that equation is ...

  y = (y2 -y1)/(x2 -x1)(x -x1) + y1

For the given points, the equation is ...

  y = (87 -55)/(4 -2)(x -2) + 55

  y = 16(x -2) +55

  y = 16x +23

Compare this to the slope-intercept form

  y = mx + b

and you see that the slope (m) is 16, and the intercept (b) is 23.

- "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."

answer: y = 3/2 x - 3

y = 1/8 x - 3/4 that would be your correct option

step-by-step explanation: w