What do the following two equations represent? y=-3x+1 y+5= -3(x-2) a) the same line b) distance parallel lines c) perpendicular lines d) intersecting, but not perpendicular lines

  a) the same line

Step-by-step explanation:

The first equation is the "slope-intercept form" of the equation of a line with slope -3 and y-intercept +1. The second equation is the "point-slope form" of the equation of the same line. The "point" in this form is (x, y) = (2, -5), which is a point that satisfies the first equation:

   y = -3x +1

  -5 = -3(2) +1  .  .  .  . true

The two equations represent the same line.

i can answer this question sweetie!

step-by-step explanation:

- "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."