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Algebra/Finding an equation in a line and an equation in slope intercept form

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Question
Find an equation of a line:
(4,-5), (1,-4)
can you show step by step please?

Find an equation in slope intercept form for the line described:
passing through the origin with no slope.

having an x-intercept -4 and parallel to the y-axis.

having an x-intercept 4 and y-intercept 3.

passing through points (1,4) and (-3,4).

passing through points (-2,3) and (-2,6).


can you explain how to get the answers for these please?

Answer
the standard equation is y = mx+b where m is the slope and b is the y-intercept
so put those values in and you have -5 = m(4)+b and -4 = m(1)+b
giving m = -1/3, b = -11/3 and the equation is y = (-1/3)x -11/3
passing through the origin with no slope, y=0
x = -4
y = (-3/4)x+3
y = 4
x = -2

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