Find the equation of the line y=mx through the origin that describes the proportional relationship shown in the graph.
line passes through y1x3 y2x6 y3x9
To find the equation of the line that passes through the origin and describes the proportional relationship shown in the graph, we need to find the slope of the line.
The slope of a line is given by the formula m = (y2 - y1) / (x2 - x1).
Using the points provided, we have:
x1 = 3, y1 = 1
x2 = 6, y2 = 2
x3 = 9, y3 = 3
Substituting these values into the slope formula:
m = (2 - 1) / (6 - 3) = 1/3
So, the slope of the line is 1/3.
The equation of a line in slope-intercept form is given by y = mx, where m is the slope.
Substituting the value of m into the equation, we have:
y = (1/3)x
Therefore, the equation of the line is y = (1/3)x.
To find the equation of the line y = mx through the origin, we need to determine the value of the slope, m.
We can find the slope by selecting any two points on the line. Here, the points are (x1, y1) = (3, 9) and (x2, y2) = (6, 18), as the line passes through them.
The slope (m) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates, we get:
m = (18 - 9) / (6 - 3)
m = 9 / 3
m = 3
So, the slope of the line is 3.
Now we can write the equation of the line y = mx through the origin, using the slope-intercept form:
y = mx
Substituting m = 3, we get:
y = 3x
Hence, the equation of the line that describes the proportional relationship shown in the graph is y = 3x.
To find the equation of the line that passes through the origin (0, 0) and describes the proportional relationship shown in the graph, we can use the given points on the line (y1, x1), (y2, x2), and (y3, x3).
First, we need to find the slope of the line (m). The slope can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Let's calculate the slope:
m = (6 - 3) / (x2 - x1)
Since the line passes through the origin, the x-coordinate of the origin is 0 and the y-coordinate is 0. So we have:
0 = m * 0
Since any number multiplied by zero is zero, we can determine that the slope (m) is 0. Therefore, the equation of the line through the origin is y = 0x or simply y = 0.