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Question 280564: Graph the equation and identify the y-intercept: 4y+5x= -12. The y-intercept is?
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! First, get the equation into slope-intercept form: y = mx + b
4y + 5x = -12
subtract 5x from both sides
4y = -5x -12
divide both sides by 4
y = -5/4x -12/3
y = -5/4x -4
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Recall,
the x-intercept is the point where y=0 and
the y-intercept is the point where x=0.
Thinking visually, the point (0, ??) will be on y-axis somewhere; likewise the point (??, 0) will be on the x-axis somewhere. Since we're drawing a line, it will cross at these points.
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To find the y-intercept, simply set x=0:
the y-intercept is -4, which is at the point (0,-4)
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Thinking about the slope-intercept equation, we know the slope is the coefficient of x.
In this case the slope is -5/4, which means it slopes downward from the upper left to the lower right.
We can find the x-intercept by setting y=0 and working it out.
0 = -5/4x -4
adding 5/4x to both sides
5/4x = -4
multiply both sides by 4
5x = -16
divide both sides by 5
x = -16/5
so the x-intercept is (-16/5, 0)
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Now you have two points: (0,-4) and (-16/5,0).
With two points you can draw line.
Plot the two points and graph the equation.
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A good check is to find another point and verify it is on the line.
Say x= -4, which neatly cancels the denominator...
y = -5/4(-4) -4
y = 20/4 -4
y = 5 -4
y = 1
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Is the point (-4,1) on the line?
Yes, it is.
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Done.
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