Question 112876
Write the equation of the line passing through each of the given pairs of points. Write your result in slope-intercept form, where possible.
(-1, 3) and (4,-2) 
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First find the slope using the slope (m) equation: m = {{{((y2-y1))/((x2-x1))}}}
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In your problems we will assign the coordinates as follows:
x1 = -1; y1 = 3; x2 = 4; y2 =-2
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Substitute these in the slope equation:
m = {{{((-2 -3))/((4 - (-1)))}}} = {{{((-2 -3))/((4 +1))}}}; minus a minus = plus
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m = {{{(-5)/5}}} = -1 is the slope
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Next use the point/slope equation which is y - y1 - m(x - x1)
We know x1 y1 and m, substitute these in the equation

y - 3 = -1(x - (-1)
y - 3 = -1(x + 1)
y - 3= -x - 1
y = -x - 1 + 3
y = -x + 2 is the slope intercept form
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You can confirm this by substituting the given values for x and see if the equal the give values for y
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Note that the intercept (which is the y intercept) always occurs when x = 0
Therefore in this equation the y intercept is +2
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The x intercept occurs when y = 0, use the equation to find that
-x + 2 = 0
-x = -2
x = +2; x has to positive, multiply equation -1 if necessary
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If you graphed this, it's even more apparent.
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{{{ graph( 300, 200, -5, 5, -10, 10, -x+2) }}} 
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How about this? Did it shed some light on this stuff