(3, 9) (2, 6) (1, 3)

Question

Write the equation of the line y=mx through the origin that describes the proportional relationship shown in the graph.

Answer 1

To find the equation of the line, we first need to find the slope (m).

The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:

m = (y2 - y1) / (x2 - x1)

From the given points: (3, 9) and (1, 3), we can find the slope as:

m = (3 - 9) / (1 - 3)
m = -6 / -2
m = 3

Since the line passes through the origin (0, 0), we can use the point-slope form of the equation for a line:

y - y1 = m(x - x1)

Plugging in the slope (m = 3) and the point (0, 0) for (x1, y1):

y - 0 = 3(x - 0)
y = 3x

Therefore, the equation of the line y = mx through the origin that describes the proportional relationship shown in the graph is y = 3x.

Answer 2

x y (x, y)
0 (0, )
4 (4, )
8 (8, )
Complete the ordered pairs in the table by finding the y-coordinate of the ordered pairs for the equation y=14x.

(2 points)
x y (x, y)
0 (0,
)
4 (4,
)
8 (8,
)

Answer 3

To find the y-coordinate of the ordered pairs, we can substitute the given x-values into the equation y = 14x.

For x = 0:
y = 14(0) = 0

For x = 4:
y = 14(4) = 56

For x = 8:
y = 14(8) = 112

Therefore, the completed ordered pairs are:
(0, 0)
(4, 56)
(8, 112)