I have 2 questions that I need help with if someone could please help me step by step to figure out how to do this equation it would be very helpful. Thank you
1. Suppose y varies directly with x and, y=15 and x=5. Write a direct variation equation that relates x and y. What is the value of y when x=9?
2. Write the equation in standard form using integers (no fractions or decimals.): y=-2/3x-1
I'm not really sure at all with this one is it
y=-2/3(0)-1
Thank you
1. When X = 5, Y = 3*5 = 15. Since Y varies directly with X, Y will ALWAYS be 3 times X: Y = 3x.
2. Slope-Intercept Form: Y = (-2/3)x - 1.
Multiply both sides by 3:
3y = -2x - 3,
Add 2x to both sides:
2x + 3y = -3,
Of course! I will be happy to help you step by step to solve your questions.
1. In this question, you are given that y varies directly with x. This means that y and x are related by the equation y = kx, where k is a constant of variation.
To find the direct variation equation that relates x and y, you need to determine the value of k.
Given that y = 15 and x = 5, substitute these values into the equation y = kx:
15 = k * 5
To isolate k, divide both sides of the equation by 5:
15/5 = k
3 = k
Therefore, the direct variation equation relating x and y is y = 3x.
Now, to find the value of y when x = 9, substitute x = 9 into the equation:
y = 3(9)
y = 27
So, when x = 9, y = 27.
2. In this question, you are given the equation y = -2/3x - 1, and you are asked to write it in standard form using integers.
The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A is positive.
To rewrite the equation y = -2/3x - 1 in standard form, we need to clear any fractions or decimals:
First, let's eliminate the fraction. Multiply every term in the equation by 3 to get rid of the denominator:
3y = -2x - 3
Next, let's eliminate the negative sign in front of x:
2x + 3y = -3
Finally, rearrange the equation so that the terms are in the order of Ax + By = C and all coefficients are integers:
2x + 3y + 3 = 0
Therefore, the equation in standard form using integers is 2x + 3y + 3 = 0.
Please let me know if there's anything else I can assist you with.