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.

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) (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:
m is the slope of the line.
Direct variation:
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:
The slope (m) is 4 and the y-intercept (b) is 3.
Direct variation:
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:

Now let's graph these two lines and compare them.

The red line is:
The green line is:
Conclusion:
The constant of variation in a direct-variation equation is the slope of the line when the equation is graphed.
RELATED QUESTIONS
is this a direct variation? ---> 2x + 3y=0 and if so what is the constant of variation?... (answered by robertb)

Find the constant of variation and the slope of the direct variation model: (answered by jim_thompson5910)

Each ordered pair is a solution of a direct variation. Write the equation of direct... (answered by stanbon)

Please help me with the following problem, the directions read: Graph the equation.... (answered by scott8148)

Is the equation in direct variation? If not, explain why. If so, what is the constant... (answered by stanbon)

what is the slope of the direct variation y=-2/3x?? how do you find it. what is the... (answered by stanbon)

Is each equation a direct variation? If it is, find the constant of variation.... (answered by jim_thompson5910)

I need help with this problem In Exercises 14-29, y varies directly as x. Find the... (answered by stanbon)

y varies directly as x. find the constant of variation and the direct-variation equation. (answered by stanbon)