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 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.
(1 point)
To find the equation of the line y=mx, we need to find the slope (m) of the line.
The slope of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
In this case, the points are (1, 4) and (2, 8).
So, m = (8 - 4) / (2 - 1) = 4 / 1 = 4.
Therefore, the equation of the line y=mx is y = 4x.
To find the equation of the line y=mx through the origin, we need to determine the slope (m) of the line.
From the information given, we know that the line passes through the points (1,4) and (2,8).
The slope (m) of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates of the points (1,4) and (2,8), we have:
m = (8 - 4) / (2 - 1)
m = 4 / 1
m = 4
Therefore, the slope (m) of the line is 4.
The equation of a line through the origin (0,0) with slope (m) is given by:
y = mx
Substituting the value of m = 4, we have:
y = 4x
Thus, the equation of the line y=mx through the origin that describes the proportional relationship shown in the graph is y = 4x.
To find the equation of the line y = mx through the origin, we need to determine the slope of the line.
In the given illustration, we can see that the line passes through the points (1, 4) and (2, 8).
The slope of a line can be found by using the formula:
slope (m) = (change in y) / (change in x)
Let's calculate the change in y:
change in y = 8 - 4 = 4
Now, let's calculate the change in x:
change in x = 2 - 1 = 1
Now, substitute the values we found into the formula to calculate the slope:
slope (m) = (change in y) / (change in x) = 4/1 = 4
Therefore, the slope of the line is 4.
Now, we can write the equation of the line y = mx through the origin, where m is the slope:
y = 4x
Hence, the equation of the line y = mx through the origin that describes the proportional relationship shown in the graph is y = 4x.