Use the image to answer the question.
An illustration shows a coordinate plane with 4 quadrants. The x-axis ranges from negative 9 to 9 in one unit increments, and the y-axis ranges from negative 11 to 11 in one unit increments. A line is graphed on the plane. An upward slanting line passes through points plotted at left parenthesis 1 comma 4 right parenthesis and left parenthesis 2 comma 8 right parenthesis.
Find the equation of the line y=mx through the origin that describes the proportional relationship shown in the graph.
(1 point)
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To find the equation of the line, we need to determine the slope, m.
The slope of a line can be found using the formula:
m = (change in y) / (change in x)
From the points given, we can see that as x increases by 1 unit (from 1 to 2), y increases by 4 units (from 4 to 8).
So, the change in y is 4 and the change in x is 1.
Therefore, the slope (m) is:
m = 4/1 = 4
As the line passes through the origin (0,0), we can substitute the slope (m) into the equation y = mx.
So, the equation of the line is:
y = 4x
To find the equation of the line y=mx through the origin, we need to determine the slope of the line from the given points (1, 4) and (2, 8).
The slope (m) of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the coordinates (1, 4) and (2, 8) into the formula:
m = (8 - 4) / (2 - 1) = 4 / 1 = 4
Therefore, the slope (m) of the line is 4.
Since the equation of the line passes through the origin (0, 0), we know that when x = 0, y = 0. Therefore, the y-intercept (b) is 0.
The equation of the line y=mx through the origin is therefore:
y = 4x