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)
To derive the equation, we can use the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept.
From the given graph, we can see that the line passes through points (3, 3) and (8, 8).
To find the slope (m), we can use the formula:
m = (y₂ - y₁) / (x₂ - x₁)
= (8 - 3) / (8 - 3)
= 5 / 5
= 1
Since the line passes through the origin (0, 0), the y-intercept, b, is 0.
Therefore, the equation is y = mx becomes y = 1x, or simply y = x.