what is the constant of variation, k, of the line y=kx through (3,18) and (5,30)?\n○ \\(\frac{3}{5}\\)\n○…
what is the constant of variation, k, of the line y=kx through (3,18) and (5,30)?\n○ \\(\frac{3}{5}\\)\n○ \\(\frac{5}{3}\\)\n○ 3\n○ 6
Answer
Explanation:
Step1: Recall the formula for direct variation
The equation is ( y = kx ), so we can solve for ( k ) by rearranging to ( k=\frac{y}{x} ).
Step2: Use the first point (3, 18)
Substitute ( x = 3 ) and ( y = 18 ) into ( k=\frac{y}{x} ). So ( k=\frac{18}{3}=6 )? Wait, no, wait, let's check the second point. Wait, (5,30): ( k=\frac{30}{5}=6 )? Wait, but the option 6 is there, but also 3? Wait, no, wait, maybe I made a mistake. Wait, (3,18): ( 18 = k\times3 ), so ( k = 18\div3 = 6 ). (5,30): ( 30 = k\times5 ), so ( k = 30\div5 = 6 ). Wait, but the option 6 is an option. Wait, but the selected option in the image is 3? Wait, no, maybe I misread. Wait, the points are (3,18) and (5,30). Let's recalculate. For (3,18): ( k = y/x = 18/3 = 6 ). For (5,30): ( k = 30/5 = 6 ). So the constant of variation ( k ) is 6? Wait, but let's check again. Wait, the equation is ( y = kx ), so it's a direct variation, so the slope is ( k ). The slope between (3,18) and (5,30) is ( (30 - 18)/(5 - 3) = 12/2 = 6 ). So ( k = 6 ).