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.
To find the equation of the line through the origin that describes the proportional relationship shown in the graph, we need to find the slope, which is represented by the variable m.
The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)
In this case, the line passes through the points (1, 4) and (2, 8). So we have:
x₁ = 1, y₁ = 4
x₂ = 2, y₂ = 8
Substituting these values into the slope formula:
m = (8 - 4) / (2 - 1) = 4 / 1 = 4
Therefore, the slope of the line is 4.
Since the line passes through the origin (0, 0), we can use the slope-intercept form of a line equation: y = mx + b.
Substituting the slope (m = 4) and the coordinates of the origin (x = 0, y = 0) into the equation, we get:
0 = 4(0) + b
0 = 0 + b
b = 0
So the equation of the line y = mx that describes the proportional relationship shown in the graph is:
y = 4x