In the coordinate plane below the equation of the line that passes through the points O (0,0) and A (1,n) is :
I need help, if anyone would be so kind to help I only have 10 min. left to submit!
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To find the equation of the line that passes through two given points, we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) represents one of the given points and m is the slope of the line.
In this case, the given points are O(0,0) and A(1,n). To find the slope (m), we need to calculate the change in y divided by the change in x between these two points.
Change in y = y2 - y1 = n - 0 = n
Change in x = x2 - x1 = 1 - 0 = 1
So, the slope (m) of the line passing through O(0,0) and A(1,n) is n/1, which simplifies to n.
Now we have the slope (m = n) and a point (A = (1, n)) that lies on the line. We can use the point-slope form to write the equation of the line as follows:
y - y1 = m(x - x1)
y - n = n(x - 1)
Expanding and simplifying, we get:
y - n = nx - n
y = nx - n + n
y = nx
Therefore, the equation of the line passing through O(0,0) and A(1,n) is y = nx.