Y=3,3 X=8,8. Use the graph to derive the equation y=mx for a line through the origin. Simplify the numerical coefficient, if needed.
To find the equation of a line through the origin, we need to determine the slope of the line.
The slope (m) of any 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 two given points are (3,3) and (8,8). Plugging in these coordinates, we get:
m = (8 - 3) / (8 - 3) = 5 / 5 = 1
The slope of the line through the origin is 1.
Therefore, the equation of the line through the origin is:
y = mx = 1x = x
To derive the equation of a line through the origin using the given points, we can first calculate the slope of the line. The slope (m) can be determined using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Using the coordinates (x₁, y₁) = (3,3) and (x₂, y₂) = (8,8), we substitute these values into the formula:
m = (8 - 3) / (8 - 3)
m = 5 / 5
m = 1
Therefore, the slope (m) is 1.
The equation of a line passing through the origin is given by y = mx, where m represents the slope. Plugging in the value of m, the equation becomes:
y = 1x
y = x
Thus, the equation of the line passing through the origin based on the given points is y = x.
To derive the equation y = mx for a line through the origin, we need to find the slope (m) of the line.
Given two points on the line, (3,3) and (8,8), we can calculate the slope using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates of the points, we get:
m = (8 - 3) / (8 - 3)
m = 5 / 5
m = 1
Therefore, the slope of the line is 1.
Since the line passes through the origin (0,0), we can write the equation as:
y = mx
Substituting the value of m, we have:
y = 1x
Simplifying, the equation becomes:
y = x