Use the image to answer the question 3;3 8;8
Use the graph to derive the equation y = mx for a line through the origin simplify the numerical coefficient if needed
y= 8x
y=x
y = 3/3x
y= 3x
Based on the image, the line that passes through the origin and goes through the points (3, 3) and (8, 8) can be described by the equation y = 1x, which simplifies to y = x.
Use the image to answer the question 1:12 2:24 3:36
The proportional relationship between inches and feet is displayed on the graph Derive the equation of the line through the origin
Based on the image, we can see that for every 1 inch, there are 12 feet. Therefore, the equation of the line through the origin is y = 12x.
Based on the given image, we can see two points labeled as (3,3) and (8,8) on a graph. These two points lie on a line passing through the origin.
To derive the equation of this line in the form y = mx, where m is the slope of the line, we need to find the value of m.
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)
In this case, we can substitute the coordinates (3,3) and (8,8) into the formula:
m = (8 - 3) / (8 - 3)
m = 5 / 5
m = 1
So, the slope of the line passing through these two points, that is, the coefficient (m) in the equation y = mx, is 1.
Therefore, the equation of the line passing through the origin can be simplified to:
y = 1x
or simply
y = x
To derive the equation y = mx for a line through the origin using the given graph, you can observe the slope of the line.
In the given graph, we have two points: (3, 3) and (8, 8). The x-coordinate of the first point is equal to the y-coordinate of the second point (3 = 3), which indicates that the line passes through the origin (0, 0).
To calculate the slope (m) of the line, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the values from the two points, we get:
m = (8 - 3) / (8 - 3)
m = 5 / 5
m = 1
Therefore, the equation of the line through the origin is y = 1x or simply y = x.