what other points are on the line of direct variation through (5, 12)? check all that apply.\n(0, 0)\n(2.5…

Explanation:

Step1: Find the constant of variation (k).

A line of direct variation is given by $y = kx$. Using the point $(5, 12)$: $$12 = k \times 5$$ $$k = \frac{12}{5}$$

Step2: Write the equation of the line.

The equation of the line of direct variation is: $$y = \frac{12}{5}x$$

Step3: Check each point.

Check if each point $(x, y)$ satisfies the equation $y = \frac{12}{5}x$, or equivalently, if $\frac{y}{x} = \frac{12}{5}$ (for $x \neq 0$).

• (0, 0): Lines of direct variation pass through the origin. $0 = \frac{12}{5} \times 0$. True.
• (2.5, 6): $y = \frac{12}{5} \times 2.5 = \frac{12}{5} \times \frac{5}{2} = 6$. True.
• (3, 10): $y = \frac{12}{5} \times 3 = \frac{36}{5} = 7.2 \neq 10$. False.
• (7.5, 18): $y = \frac{12}{5} \times 7.5 = \frac{12}{5} \times \frac{15}{2} = \frac{180}{10} = 18$. True.
• (12.5, 24): $y = \frac{12}{5} \times 12.5 = \frac{12}{5} \times \frac{25}{2} = \frac{300}{10} = 30 \neq 24$. False.
• (15, 36): $y = \frac{12}{5} \times 15 = 12 \times 3 = 36$. True.

Answer:

(0, 0) (2.5, 6) (7.5, 18) (15, 36)