Question

write the equation of the proportional relationship.
(grid with x and y axes, x from 0 to 10, y from 0 to 10, line through origin and (1,3) - looking at the grid, when x=1, y=3? wait, no, looking at the grid, lets check points. wait the line goes through (0,0) and lets see, when x=1, y=3? wait no, the grid: x-axis labels 0,2,4,6,8,10; y-axis 0,2,4,6,8,10. wait the line: from (0,0) to, say, x=1, y=3? wait no, maybe x=1, y=3? wait the equation is y = x. so we need to find the slope (constant of proportionality) by taking a point on the line. lets pick a point: when x=1, whats y? wait the grid has squares, so each square is 1 unit? wait the line passes through (1,3)? wait no, looking at the image, the line goes from (0,0) up, so lets see, when x=1, y=3? wait maybe x=1, y=3? wait the problem is to write y = kx, find k. so take a point: for example, when x=1, y=3? wait no, maybe x=2, y=6? so 6/2=3, so k=3. so the equation is y=3x. but the ocr text is: \write the equation of the proportional relationship.\ with the grid and y = x.

Explanation:

Step1: Recall proportional form

Proportional equations follow $y=kx$, where $k$ is the constant of proportionality (slope).

Step2: Pick a point on the line

Choose a clear point, e.g., $(2,6)$.

Step3: Solve for $k$

Substitute $x=2$, $y=6$ into $y=kx$:
$6 = k \times 2$
$k = \frac{6}{2} = 3$
Verify with another point, e.g., $(3,9)$: $9 = 3 \times 3$, which holds true.

Answer:

$y=3x$