Suppose y varies directly with x, and y = 19/3when x =4/5. What direct variation equation relates x and y? What is the value of y when x = -7/6
The direct variation equation relating x and y can be written as y = kx, where k is the constant of variation. We can solve for k using the given values of y and x.
Since y varies directly with x, we have (19/3) = k(4/5).
To solve for k, we multiply both sides of the equation by (5/4):
(19/3) * (5/4) = k * (4/5) * (5/4)
(19/3) * (5/4) = k
(95/12) = k
Therefore, the equation relating x and y is y = (95/12)x.
To find the value of y when x = -7/6, we substitute this value into the equation:
y = (95/12) * (-7/6)
y = -665/72
To determine the direct variation equation that relates x and y, we can use the formula for direct variation, which states that y varies directly with x if it can be written in the form y = kx, where k is the constant of variation.
Given that y = 19/3 when x = 4/5, we can substitute these values into the equation to solve for k.
19/3 = k * (4/5)
To solve for k, we can cross multiply and get:
19 * 5 = 3 * 4k
95 = 12k
Divide both sides by 12:
k = 95/12
So the direct variation equation that relates x and y is:
y = (95/12) * x
To find the value of y when x = -7/6, we can substitute this value into the equation:
y = (95/12) * (-7/6)
To simplify the expression, we can cancel out common factors:
y = (95 * -7) / (12 * 6)
y = -665 / 72
Therefore, the value of y when x = -7/6 is -665/72.
To find the direct variation equation relating x and y, we need to first determine the constant of variation (k). The direct variation equation is of the form y = kx, where k is the constant of variation.
Given that y varies directly with x, we can set up a proportion using the known values:
y / x = k
To find the value of k, we can substitute the given values y = 19/3 and x = 4/5 into the proportion:
(19/3) / (4/5) = k
Simplifying this expression, we get:
(19/3) * (5/4) = k
95/12 = k
Now that we have the value of k, we can write the direct variation equation relating x and y:
y = (95/12) * x
To find the value of y when x = -7/6, we substitute x = -7/6 into the direct variation equation:
y = (95/12) * (-7/6)
Simplifying this expression, we obtain:
y = -665/72
Therefore, when x = -7/6, the value of y is -665/72.