Graphing Linear Equations Unit Test
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Question
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 5 right parenthesis and left parenthesis 2 comma 10 right parenthesis.
The graph shows the proportional relationship. Derive the equation of the line y=mx through the origin.
(1 point)
To find the equation of the line y = mx that passes through the origin, we need to find the slope (m) of the line.
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:
m = (y2 - y1) / (x2 - x1)
In this case, the points are (1, 5) and (2, 10). Plugging these values into the formula:
m = (10 - 5) / (2 - 1)
m = 5 / 1
m = 5
Therefore, the equation of the line y = mx passing through the origin with slope 5 is:
y = 5x