To find a line that goes through two given points first find the slope between the points. (y-y)over (x-x) Then use a formula to find the rest.
I use the slope intercept formula and find "b" the y-intercept.
Let's try one.
(2,7) and (3,10)
7-10=-3
2-3=-1
-3/-1=3 the slope
7=3(2)+b
7=6+b
7-6=b
1=b
SO y=3x+1 is the formula for a line going through (2,7) and (3,10)
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By substitution
Subtract the equation of one line from the equation of the other
The x and y coordinates
Substitute the coordinates of the point into the equation of the line. If the result is true, then the point is on the line.
The graph (on Cartesian coordinates) of a quadratic equation is a parabola.