Write an equation in standard form for the line that passes through (3,-1) and (-5,-3)

0 = x - 4y - 7

Step-by-step explanation:

Moving from (-5, -3) to (3, -1), we see that x (the run) increases by 8 and y (the rise) incrases by 2.  Thus, the slope of the line connecting these two points is m = rise / run = 2/8, or 1/4.

Use the slope-intercept form of the equation of a straight line first:

y = mx + b becomes          -1 = (1/4)(3) + b, or (after multiplying all three terms

                                           by 4)  -4 = 3 + 4b.  Then 4b = -7, and b = -7/4.

Then the desired equation is    y  = (1/4)x - 7/4, or

4y = x - 7, or

0 = x - 4y - 7.  This is the desired equation in standard form.

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