(3, 9) (2, 6) (1, 3)
Write the equation of the line y=mx through the origin that describes the proportional relationship shown in the graph.
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,
)
To find the equation of the line that describes the proportional relationship shown in the graph, we can use the coordinates of two points on the line. In this case, we have the points (3, 9) and (2, 6).
The equation of a line in slope-intercept form is y = mx + b, where m represents the slope of the line and b represents the y-intercept.
Since the line passes through the origin (0, 0), the y-intercept is 0. Hence, the equation of the line becomes y = mx.
To find the slope (m), we can use the formula:
m = (y2 - y1) / (x2 - x1)
Let's use the points (3, 9) and (2, 6) to calculate the slope:
m = (6 - 9) / (2 - 3) = -3 / -1 = 3
Therefore, the equation of the line y = mx through the origin is y = 3x.
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.
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)
To find the equation of the line y = mx through the origin, we need to calculate the slope of the line using the given points.
The slope (m) can be determined using the formula:
m = (y2 - y1) / (x2 - x1)
Let's choose any two points from the given points.
Using (1, 3) and (2, 6):
m = (6 - 3) / (2 - 1)
m = 3 / 1
m = 3
Now that we have the slope (m) as 3, we can substitute it into the equation y = mx to get the equation of the line:
y = 3x