Graph the line that represents a proportional relationship between y and x where the unit rate of change of y with respect to x is 4/5. In other words, a change of 1 unit in x corresponds to change of 4/5 units in y. Graph the line and write the equation of the line.

The required line is will be:

The graph of the line y = 4/5x is attached below.

Step-by-step explanation:

We know that when y varies directly with x, we get the equation

y ∝ x

y = kx

k = y/x

where k is called the 'constant of variation'.

It is also clear that 'constant of variation' basically represents the slope m or rate of change, with the lines passing through the origin, so

given

k = 4/5

substitute k = 4/5 in the equation y = kx

y = kx

y = 4/5x

Therefore, the required line is will be:

The graph of the line y = 4/5x is attached below.

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)