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determine the slope and the y intercept 10x+y+12=0

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3 Answers

Rewrite the equation in slope-intercept form, y = mx + b, where m is the slope and b is the y value of the y intercept. Then, the slope is the change in the y values divided by the change in the x values.
 
m = (y2 - y1)/(x2 - x1) = [(mx2 + b) - (mx1 + b)]/(x2 - x1)
 
But, this is just [m(x2 - x1) + (b - b)]/(x2 - x1), or
 
m(x2 - x1)/(x2 - x1) = m
In order to answer this question, FIRST you need to write the equation ins slope intercept form.
 
Slope intercept is y = mx + b
                          
                               the "m" is the slope
                               the "b" is the y interccept
 
So, let's put this in slope intercept form, by keeping y on one side by itself. We must move the 12 to the opposite side of the equation first, then I can rewrite the equation with the y on the left.
 
        10x = y+12
10x - 12 = y + 12 - 12   (I am subtracting 12 from BOTH sides)
 10x -12=y                   (the 12 cancels out so I have only y left)
         y=10x-12            (remember the equation is interchangeable. If 3 + 2 = 5, then 5 = 3 +2. I can do                                    the  same with slope intercept form)
 
So, now that the equation is in slope intercept form, I can see that 10 is where the "m" goes, so the slope is 10. I can see that -12 is where the "b" goes, so the y intercept is -12.
10x + y + 12 = 0
10x + y +12 -12 = -12
10x +y = -12
10x + y -10x = -12 -10x
y = -10x -12
 
The slope of the line will be -10, and y-intercept will be -12