Answer :
Answer: The slope of the line is 15 and y-intercept is 12.
Step-by-step explanation: We are given to find the slope and y-intercept of the straight line defined by the points (3, 57) and (5, 87).
We know that
the slope of a line passing through the points (3, 57) and (5, 87) is given by
[tex]m=\dfrac{87-57}{5-3}=\dfrac{30}{2}=15.[/tex]
Since the straight line passes through the point (3, 57), so its equation will be
[tex]y-57=m(x-3)\\\\\Rightarrow y-57=15(x-3)\\\\\Rightarrow y-57=15x-45\\\\\Rightarrow y=15x-45+57\\\\\Rightarrow y=15x+12.[/tex]
So, the required equation of the straight line is [tex]y=15x+12.[/tex]
Thus, the slope of the line is 15 and y-intercept is 12.