Graph the line for  y−6=−4(x+2) on the coordinate plane.

Equation of a line is given by ax+by=c=0, where is the slope of the line.

Given : y−6=−4(x+2)

⇒y-6= -4x-8[distributive property]

⇒4x+y+2=0[standard form] is the equation of line, whose slope= -4

to plot this line on the coordinate plane , we to find its points by substitution.

1. Substitute x=0 in equation, we get

y+2=0⇒y=-2

2. Substitute y=2 in equation, we get

4x+2+2=0⇒4x+4=0⇒x= -1

So we got points (0,-2)and(-1,2) to plot the line on coordinate plane.

Using this you can plot the graph as shown in picture.

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.

- "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."