Graphed line Points:
(3, 1), (6, 2), (9, 3)
Write the equation of the line y=mx through the origin that describes the proportional relationship shown in the graph.
To find the equation of the line through the origin, we need to find the slope (m) of the line.
We can find the slope using any two of the points given. Let's use the points (3, 1) and (6, 2):
m = (y2 - y1) / (x2 - x1)
m = (2 - 1) / (6 - 3)
m = 1 / 3
Now that we have the slope (m), we can write the equation of the line through the origin:
y = mx
y = (1/3)x
So, the equation of the line that describes the proportional relationship shown in the graph is y = (1/3)x.
From the equation y = x, we can see that the line passes through the origin (0, 0) and that for every x value, there is a corresponding y value that is equal to x.
Therefore, the line passes through all points where y = x. This means that the ordered pair (3, 3) will also satisfy the equation y = x.
So, the additional ordered pair that satisfies the equation y = x when x = 3 is (3, 3).
Graphed line Points:
(0, 0), (1, 1), (2, 2)
Use the graph of y=x to determine an additional ordered pair (x, y) that satisfies the equation. Find the ordered pair (x, y) if the x -coordinate is 3.
Graphed line Points:
(3, 3), (8, 8)
Use the graph to derive the equation y=mx for a line through the origin. Simplify the numerical coefficient, if needed.
To derive the equation of the line through the origin with the given points (3, 3) and (8, 8), we need to find the slope (m) first.
m = (y2 - y1) / (x2 - x1)
m = (8 - 3) / (8 - 3)
m = 5 / 5
m = 1
Now that we have the slope (m), we can write the equation of the line through the origin:
y = mx
y = 1x
y = x
Therefore, the equation of the line through the origin that describes the relationship shown in the graph is y = x.
Graphed line Points:
(0, 0), (5, 1)
Use the graph to derive the equation y=mx for a line through the origin. Simplify the numerical coefficient, if needed.
To find the equation of the line through the origin with the given points (0, 0) and (5, 1), we first need to find the slope (m).
m = (y2 - y1) / (x2 - x1)
m = (1 - 0) / (5 - 0)
m = 1 / 5
Now that we have the slope (m), we can write the equation of the line through the origin:
y = mx
y = (1/5)x
Therefore, the equation of the line through the origin that describes the relationship shown in the graph is y = (1/5)x.