SOLUTION: Find the equation, in slope-intercept form, of the line that passes through the points (5, 2) and (-7, 3). Write the equation in slope-intercept form.

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One way to do it (not the only way) is this:
Write the general slope-intercept equation
where is the slope
and is the y-intercept
The line in the problem passes through
(5,2) and (-7,3)
Substitute the 1st point in the general equation
(1)
Substitute the 2nd point in the general equation
(2)
You have 2 unknowns and 2 equations, so it's solvable
Subtract (1) from (2)


Substitute this in (1)



Now plug and back into the general equation
answer
Check to see if the line passes through (5,2) and (-7,3)



and



OK