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
The first step is to find the slope of the line. The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Using the given points (1, 5) and (2, 10), we can calculate the slope:
m = (10 - 5) / (2 - 1) = 5 / 1 = 5
Now that we have the slope, we can use the equation of a line in slope-intercept form:
y = mx
Since the line passes through the origin, the y-intercept is 0. Therefore, the equation of the line is:
y = 5x