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=8x
y equals 8 x
y=x
y equals x
y=33x
y equals Start Fraction 3 over 3 End Fraction x
To determine the equation y=mx for a line through the origin, we need to find the slope of the line on the graph. The slope can be found by calculating the change in y divided by the change in x between two points on the line.
From the graph, we can see that the line passes through the points (3,3) and (8,8). The change in y is 8 - 3 = 5, and the change in x is also 8 - 3 = 5.
Therefore, the slope (m) of the line is 5/5 = 1.
The equation y = mx for a line through the origin is y = 1x, which simplifies to y = x.
So, the correct answer is: y = x