a) Determine the functions whose graphs are parallel to the graph of the function y=0.5x+10 and intersect the graph of the function y= -1.5x. The functions are expressed by the formulas.

y = -1.5x + 6, y = 0.5x-6

b) Determine the functions whose graphs are parallel to the graph of the function y=0.5x+10 and intersect the graph of the function y= -1.5x. The functions are expressed by the formulas.

y = 0.5x+4, y = 0.5x, y = 3+1.5x

a) The function that is parallel to the function [tex]y = 0.5\cdot x + 10[/tex] and intercept the function [tex]y = -1.5\cdot x[/tex] is [tex]y = 0.5\cdot x - 6[/tex].

b) The functions that are parallel to the function [tex]y = 0.5\cdot x + 10[/tex] and intercept the function [tex]y = -1.5\cdot x[/tex] are [tex]y = 0.5\cdot x + 4[/tex] and [tex]y = 0.5\cdot x[/tex].

Linear functions are expressions of the following form:

[tex]y = m\cdot x + b[/tex] (1)

Where:

[tex]x[/tex] - Independent variable.
[tex]y[/tex] - Dependent variable.
[tex]m[/tex] - Slope.
[tex]b[/tex] - y-Intercept.

Two lines are parallel if and only if they have the same slope but distinct intercepts. and two lines intercept each other when they have distinct slopes. Now we proceed to present the solution for each point:

a) The function that is parallel to the function [tex]y = 0.5\cdot x + 10[/tex] and intercept the function [tex]y = -1.5\cdot x[/tex] is [tex]y = 0.5\cdot x - 6[/tex].

b) The functions that are parallel to the function [tex]y = 0.5\cdot x + 10[/tex] and intercept the function [tex]y = -1.5\cdot x[/tex] are [tex]y = 0.5\cdot x + 4[/tex] and [tex]y = 0.5\cdot x[/tex].

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