The graph shows the proportional relationship. Derive the equation of the line y=mx through the origin.
(5,1) (10,2)
To derive the equation of the line y=mx through the origin using the points (5,1) and (10,2), we first need to calculate the slope (m) of the line.
The slope formula is given by: m = (y2 - y1) / (x2 - x1)
Using the points (5,1) and (10,2), we have:
m = (2 - 1) / (10 - 5)
m = 1 / 5
m = 0.2
Now that we have the slope, we can write the equation of the line through the origin as:
y = 0.2x
Therefore, the equation of the line y=0.2x through the origin is y = 0.2x.
Graph the proportional relationship y=2x by plotting points.
To graph the proportional relationship y=2x by plotting points, we can choose a few x-values and calculate the corresponding y-values using the equation y=2x.
Let's choose x-values of 0, 1, 2, 3, and 4 and calculate the corresponding y-values:
For x = 0:
y = 2(0) = 0
For x = 1:
y = 2(1) = 2
For x = 2:
y = 2(2) = 4
For x = 3:
y = 2(3) = 6
For x = 4:
y = 2(4) = 8
Plotting these points (0,0), (1,2), (2,4), (3,6), and (4,8) on a graph, we can see that they lie on a straight line passing through the origin and have a slope of 2. The graph of the proportional relationship y=2x will be a straight line that goes through these points.