exam Maths Puzzle Numerical Ability

will you please explain to me how to do this using an equation. i am so lost.
It says, find the slope and equation of the line through the points (-2,5) and (3,-1)
If you could help me, that would be wonderful. thank you and God bless.

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exam Other Question

Input/Output Table

Input: Output
-2 4
1 1
4 16

What is the funtion rule?
the graph of the equation y=x^2+2x-8 where does it intersect the x-axis?