13. -4 + 7x + 4 = 3y Find the constant of variation.
Someone help, I can't understand how to do it. None of the websites I look up have good explanations, help?
well, you have
7x = 3y
y = 7/3 x
7/3 is the constant of variation.
when one says y varies directly with x, it means that there is a constant k such that
y = kx
If y varies inversely as x, then there is k such that
xy = k or, y = k/x
These can be combined, so that if you hear
y varies directly as x and inversely as the square of w, it means
y = kx/w^2
Thank you! You actually explained it perfectly! Now I can get my homeowork done :3
To find the constant of variation in the equation -4 + 7x + 4 = 3y, we need to rearrange the equation into slope-intercept form, y = mx + b. Once we have it in this form, the coefficient of x will be the constant of variation.
Let's go step-by-step:
1. Start with the given equation: -4 + 7x + 4 = 3y.
2. Combine like terms on the left side: 7x = 3y.
3. Divide both sides by 3 to isolate y: (7/3)x = y.
4. The coefficient of x, which is 7/3, is the constant of variation.
So, the constant of variation in the given equation is 7/3.
To find the constant of variation, we need to rewrite the given equation in slope-intercept form (y = mx + b), where m represents the constant of variation. Let's go step-by-step:
1. Start with the given equation: -4 + 7x + 4 = 3y.
2. Combine the constants on the left side: 7x = 3y.
3. Divide both sides of the equation by 3 to isolate y: (7/3)x = y.
4. Now, the equation is in the form y = mx, where m is the constant of variation. Thus, the constant of variation is (7/3).
The constant of variation represents the ratio between the dependent variable (y) and the independent variable (x) in a linear equation. In this case, for every unit increase in x, y increases by (7/3) units.