Cora says he dosen't need to know the y-interce of a line to write its equation, just its slope and some other point on the line. is she correct? explain. if cora is correct, explain how to find the equation of a line with a slope of -1/3 that includes the point (2,6)

Yes, Cora is correct.

The equation of line with point  (2,6) and slope of line (-1/3)

is x + 3y - 20 = 0

Step-by-step explanation:

Yes, the equation of a line can be written using a point and a slope of the line equation.

Cora has used the POINT SLOPE FORMULA, to represent the line equation.

In Point Slope formula:

The equation with slope m and points (x0,y0) can be written as:

(y-y0) =m (x-x0)

Here, the point (x0,y0) = (2,6)

and slope m = (-1/3)

So, the equation can be written as:

Hence, the equation of line with point  (2,6) and slope of line (-1/3)

is x + 3y - 20 = 0

- "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."