SOLUTION: Explain how the constant of variation and the slope are related in a direct variation equation. Please help I'm stuck and need help.

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Question 24077: Explain how the constant of variation and the slope are related in a direct variation equation. Please help I'm stuck and need help.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Compare the slope-intercept form of a linear equation with an equation for direct variation.
Slope-intercept form:
y+=+mx+%2B+b m is the slope of the line.
Direct variation:
y+=+kx y varies diectly as x. k is the constant of variation.
Do you see the similarity?
Let's compare the two equations using numbers:
Slope-intercept:
y+=+4x%2B3 The slope (m) is 4 and the y-intercept (b) is 3.
Direct variation:
y+=+kx To find the value of k, you'll need to know the values of y and x. Let's say that y = 8 when x = 2, so that k = y/x = 8/2 = 4. So you can write:
y+=+4x
Now let's graph these two lines and compare them.
graph%28300%2C200%2C-5%2C5%2C-5%2C5%2C4x%2B3%2C4x%29
The red line is: y+=+4x%2B3
The green line is: y+=+4x
Conclusion:
The constant of variation in a direct-variation equation is the slope of the line when the equation is graphed.