Answers (2)
It's "point", not some goofy abbreviation that you made up. Math presentation is always carefully defined so that nobody has to guess at your meaning. Misunderstandings and spelling mistakes kill people.
Slope is rise over run. Run is horizontal distance, left to right. Run is always positive because we always go left to right. Rise is the vertical change in that same distance. A negative rise means it drops. The given line runs 2 units from 2 to 4 and rises 2 units from 3 to 5 so the slope is 2/2 = 1.
The equation of a line is y = mx where m is the slope. That line passes through the origin. If you want it to pass through some point (a, b) you subtract the coordinates like this: y - b = m(x - a). That is the point-slope form, and you can rewrite it in other forms if it is convenient. You may do this with any point on the line. They all reduce to the same equation.
y - 3 = x - 2 point-slope form
y = x + 1 slope-intercept form
-x + y - 1 = 0 standard form, all variables on the left, no fractions, and zero or a constant on the right
Second line: y - 6 = 2(x - 3)
y = 2x
Plot these so you have a picture of what you are looking for.
www.wolframalpha.com/input/?i=plot+y+%3D+x+%2B+1,+y+%3D+2x
Now you find the point of intersection. Substitute 2x for y in the first line.
2x = x + 1
x = 1, y = 2
No answer.
Line f with Points A(2,3), B(4,5)
f := y - 3 = ((5 - 3) / (4 - 2)) * (x - 2)
y = x + 1.
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Line g with Points C(6,8), D(3,2)
g := y - 8 = ((2 - 8) / (3 - 6)) * (x - 6)
y = 2x - 4.
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Intersection point P:
x + 1 = 2x - 4
x = 5 ;; x-coordinate. Insert into y = x + 1:
y = 6.
P (5, 6)
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The intersection point P is well outside the line segment AB. So, this line segment is not divided by the line joining the pt(6,8) (3,2).
But line segment [C(6,8) D(3,2)] is divided by f in P in the ratio 1: 2.