Find the equation of the line y=mx through the origin that describes the proportional relationship shown in the graph
The equation of a line through the origin is of the form y = mx, where m is the slope of the line.
In this case, we need to find the slope of the line that describes the proportional relationship shown in the graph. To do this, we can choose two points on the line and calculate the slope using the formula:
m = (y2 - y1) / (x2 - x1)
Let's choose the points (0,0) and (1, m) on the line:
m = (m - 0) / (1 - 0)
m = m / 1
m = m
Since m is the slope of the line, we can conclude that the slope is equal to m.
Therefore, the equation of the line is y = mx.
To find the equation of the line that describes the proportional relationship shown in the graph, we need to determine the value of the slope, m.
Since the line passes through the origin, we can use two points on the line: (0, 0) and another point given in the graph to find the slope.
Let's choose a point on the line. From the graph, it appears that we can use the point (2, 4).
The slope, m, can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Let's substitute the values into the formula:
m = (4 - 0) / (2 - 0)
m = 4 / 2
m = 2
Now that we have the value of the slope, we can write the equation of the line in slope-intercept form:
y = mx + b
Since the line passes through the origin, the y-intercept, b, is 0. Therefore, the equation of the line y = mx through the origin is:
y = 2x
To find the equation of a line through the origin in the form y = mx, we need to determine the slope (m) of the line.
Given that the line passes through the origin and describes a proportional relationship shown in the graph, we can determine the slope by selecting any two points on the line.
In a proportional relationship, any two points on the line will have a constant ratio between their y-coordinates and their x-coordinates. Let's choose two such points, (x1, y1) and (x2, y2), to find the slope.
Looking at the graph, find two points that lie on the line. Let's suppose one point is (x1, y1) and the other point is (x2, y2).
Once you have the coordinates of the two points, calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Substitute the values of (x1, y1) and (x2, y2) into the slope formula and calculate the value.
Once you have the value of m, you can substitute it into the equation y = mx to get the equation of the line through the origin.