Answer:
The equation of line that passes through O(0,0) and C(6,9)
[tex]y=\frac{3}{2} x[/tex].
Step-by-step explanation:
Given
In xy- plane above , the coordinates of point C =(6,9)
The coordinates of point of O=(0,0)
We know that the equation of line that passes through two points [tex](x_1,y_1) \; and (x_2,y_2)[/tex]
[tex]\frac{y-y_1}{y_1-y_2} =\frac{x-x_1}{x_1-x_2}[/tex]
[tex]x_1=0, y_1=0[/tex]
[tex]x_2=6, y_2=9[/tex]
By substituting the value of [tex]x_1,y_1,x_2 \;and \; y_2[/tex] in the above formula
The equation of line that passes through the points (0,0) and (6,9) is given by
[tex]\frac{y-0}{0-9} =\frac{x-0}{0-6}[/tex]
The equation of line that passes through the points O (0,0) and (6,9) is given by
[tex]\frac{y}{-9} =\frac{x}{-6}[/tex]
The equation of line is given by
[tex]y=\frac{3}{2} x[/tex]
Hence, the required equation of line that passes through the points O (0,0) and C(6,9)
[tex]y=\frac{3}{2} x[/tex]
The simplest equation that can contain two points is a linear equation,
Here we will find that the line equation is
[tex]y = (3/2) \cdot x[/tex]
A general linear equation is:
[tex]y = a\cdot x + b[/tex]
Such that a is the slope, and b is the y-intercept.
If we know that the line passes through the points (x₁, y₁) and (x₂, y₂), the slope can be written as:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here we know that our equation must pass through point C, (6, 9) and through point O, the origin, or just (0, 0)
Then the slope of our equation will be:
[tex]a = \frac{9 - 0}{6 - 0} = 9/6 = 3/2[/tex]
Then our equation is something like:
[tex]y = (3/2) \cdot x + b[/tex]
To find the value of b, we can use the fact that the line contains the origin (0, 0)
This means that when x = 0, we also have y = 0.
Replacing that in the above equation we get:
[tex]0 = (3/2) \cdot 0 + b\\\\0 = b[/tex]
Then the equation of the line is:
[tex]y = (3/2) \cdot x[/tex]
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