Of the following equations below, which equation represents a direct variation between x and y? Select one: A. 2y = 3x −7 B. y −4 = x +6 C. y +3 = x +3 D. 4y +1 = 4x−1
Accepted Solution
A:
Answer:C. y +3 = x +3Step-by-step explanation:We need to find in below option x has direct variation with y.We solve for each;A. [tex]2y = 3x-7[/tex]From above equation we can state that 2 times y is equal to 7 less than 3 times of x.Hence it doesn't represent direct variation. B. [tex]y-4 = x+6[/tex]Solving above expression we get;[tex]y-4 = x+6\\y = x+6+4\\y=x+10[/tex]From above equation we can state that y is equal to 10 more than x.Hence it doesn't represent direct variation. C. [tex]y+3 = x+3[/tex]Solving above expression we get;[tex]y+3 = x+3\\y = x+3-3\\y=x[/tex]From above equation we can state that y is equal to x.Hence it represent direct variation. D. [tex]4y+1 = 4x-1[/tex]Solving above expression we get;[tex]4y+1 = 4x-1\\4y = 4x-1-1\\4y=4x-2[/tex]From above equation we can state that 4 times y is equal to 2 less than 4 times of x.Hence it doesn't represent direct variation. Hence the Answer which represent direct variation of x and y is,C. [tex]y+3 = x+3[/tex]