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 slope form gives the line: 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

Correct answer:

p1 : p1:3x+2y+8=0
p2 = 0
p3 : p3: 7x+8y+19=0
p4 : p4: 2x-y+6=0

Step-by-step explanation:

x =  4 + 2p y = 2  3p  3x = 12+6p 2y = 4  6p  p1:p1:3x+2y+8=0=0:1
y = 3x  1  p2:3xy1=0=0:1
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  3a5b=19 5a2b=19  Pivot:Row1Row2 5a2b=19 3a5b=19  Row253 Row1Row2 5a2b=19 3.8b=30.4  b=3.830.4=8 a=519+2b=519+2 8=7  a=7 b=8  p3:p3:7x+8y+19=0=0:1
y=kx+q k=2  6=k 0+q 6=2 0+q  q=6  q=16=6  q=6  p4: y = 2 x+6  p4:p4:2xy+6=0=0:1

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

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