Equation of a line, use the slope intercept formula for points (3,-6) and (5,8) including a check. please help me learn instead of telling me the answer :)

i’ll show u what i have so far

y=7x-27

Step-by-step explanation:

The equation of a line is given by y=mx+C where m is the gradient of the line or slope and c is the intercept on your axis. according to your question, you are given two point on (3,-6) and (5,8). so we can get the gradient m= Y2-Y1/X2-X1= gradient. so Y1= -6, Y2=8 , X1=3, X2=5

slope= 8-(-6)/5-3=14/2=7. so m=7so the equation of line can be written in form y=7x+C. but we need to find C. C can be gotten from where the line passes through (3,-6) that is when x=3, y=-6. so we can find C from that point. -6=7(3)+C..so we have -6=21+C. C=-6-21=-27

so the equation of the line is y=7x-27

- "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."