General line equations

In all examples, write the GENERAL EQUATION OF a line that is given in some way.

A) the line is given parametrically: x = - 4 + 2p, y = 2 - 3p

B) the line is given by the slope form: y = 3x - 1

C) the line is given by two points: A [3; -3], B [-5; 2]

D) the line intersects the y-axis at point 0; 6 and has a slope k = 2

Result

p1 = (Correct answer is: ) OK
p2 = (Correct answer is: ) OK
p3 = (Correct answer is: ) OK
p4 = (Correct answer is: ) OK

Solution:

x=−4+2p y=2−3p  3x=−12+6p 2y=4−6p  p1:3x+2y+8=0
y=3x−1  p2:3x−y−1=0
ax+by+c=0 c=19    a⋅ 3+b⋅ (−5)+c=0 a⋅ (−5)+b⋅ 2+c=0 a⋅ 3+b⋅ (−5)+19=0 a⋅ (−5)+b⋅ 2+19=0  3a−5b=−19 5a−2b=19  a=7 b=8  p3:7x+8y+19=0
y=kx+q k=2    6=k⋅ 0+q 6=2⋅ 0+q  q=6  p4:y=2⋅ x+6  p4:2x−y+6=0

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Tips to related online calculators
For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc.

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