Question 1:
The generic equation of the line is given by:

Where,
m: slope of the line
b: cutting point with the y axis
Substituting values we have:
Answer: an equation for the line with slope 2/3 and y-intercept is:
Question 2:
The standard equation of the line is given by:

Where,
m: slope of the line
(xo, yo): ordered pair that belongs to the line
The slope of the line is:

Substituting values:

We choose an ordered pair:

Substituting values:

Rewriting:
Answer: An equation in slope-intercept form for the line that passes through the points (1, -3) and (3,1) is:
Question 3:
For this case, since the variation is direct, then we have an equation of the form:

Where,
k: constant of variation.
We then have the following equation:

Rewriting we have:

Therefore, the constate of variation is given by:
Answer: the constant of variation is:
Question 4: For this case, since the variation is direct, then we have an equation of the form:

Where,
k: constant of variation.
We must find the constant k, for this we use the following data:
y = 24 when x = 8
Substituting values:

Clearing k we have:

Therefore, the equation is:

Thus, substituting x = 10 we have that the value of y is given by:
Answer: the value of y when x = 10 is: