Find the equation of the line that passes through the point of intersection of x + 2y = 9 and 4x -2y = -4 and the point of intersection of intersection of the lines 3x - 4y = 14 and 3x + 7y = -8.

Step-by-step explanation:

The point of intersection of

and

is the solution of the two equations.

We add equation (1) and equation(2) to get,

We put into equation (1) to get,

Therefore the line passes through the point, .

The line also passes through the point of intersection of

and

We subtract equation (3) from equation (4) to obtain,

We substitute this value into equation (4) to get,

The line also passes through

The slope of the line is

The equation of the line is

is the required equation

- "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."