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 line passes through points plotted at left parenthesis 3 comma 3 right parenthesis and left parenthesis 8 comma 8 right parenthesis.
Use the graph to derive the equation y=mx for a line through the origin. Simplify the numerical coefficient, if needed.
(1 point)
Responses
y=3x
y equals 3 x
y=x
y equals x
y=33x
y equals Start Fraction 3 over 3 End Fraction x
y=8x
y equals 8 x
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y=x
To derive the equation y=mx for a line through the origin using the given graph, we can use the two points plotted on the line: (3, 3) and (8, 8).
First, we can calculate the slope (m) of the line using the formula:
m = (change in y) / (change in x)
In this case, the change in y is 8 - 3 = 5, and the change in x is 8 - 3 = 5.
So, the slope (m) is 5/5 = 1.
Next, we substitute the slope (m) into the equation y=mx, and since the line passes through the origin, the y-intercept (b) is 0.
Therefore, the equation y=mx for the line through the origin is:
y = 1x
Simplifying the numerical coefficient, we get:
y = x