Answer: The slopes are equal.
The points are representing the same line.
Step-by-step explanation:
We know that the slope between points (a,b) and (c,d) is given by :-
[tex]m=\dfrac{d-b}{c-a}[/tex]
The slope between the points (4,30) and (12,90) will be
[tex]m_1=\dfrac{90-30}{12-4}=\dfrac{60}{8}=\dfrac{15}{2}[/tex]
The slope between the points (4,30) and (10,75) will be
[tex]m_2=\dfrac{75-30}{10-4}=\dfrac{45}{6}=\dfrac{15}{2}[/tex]
[tex]\Rightarrow\ m_1=m_2[/tex]
We know that if the slopes are equal then the lines are parallel.
But they have one point common (4,30) so it cannot be parallel, they ust be same line .
