Q. If y varies directly with x and y=8 when x=4, find y when x=3. Write and solve a direct variation equation to find the answer.y = ___
Establish equation for direct variation: Establish the equation for direct variation.Since y varies directly with x, the equation can be written as y=kx, where k is the constant of proportionality.
Find constant of proportionality: Use the given values to find the constant of proportionality k. We are given that y=8 when x=4. Plugging these values into the direct variation equation gives us 8=k×4.
Solve for k: Solve for k.Divide both sides of the equation by 4 to isolate k.48=4k×42=k
Write equation with k: Write the direct variation equation with the found value of k. Now that we know k=2, the direct variation equation is y=2x.
Find y for x=3: Find y when x=3 using the direct variation equation.Substitute x=3 into the equation y=2x to find y.y=2×3y=6
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