I assume that is a straight line between point (0, 0) and point (3, 1):
The equation of any line is given by:
y - yo = m(x - xo)
where m is the gradient given by:
m = (y1 - yo)/(x1 - x0)
Thus, line is:
y - 0 = (1 - 0)/(3 - 0)(x - 0)
⇒ y = 1/3 x
or 3y = x
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Slope of line: 3 Perpendicular slope: -1/3 Equation: y-2 = -1/3(x-0) => y = -1/3x+2
The slope of the line is 2 and its equation is y = 2x-1
Points: (3, -6) and (-3, 0) Slope: -1 Equation: y = -x-3
Perpendicular slope: -1/4 Perpendicular equation: y-0 = -1/4(x-3) => y = -0.25x+3
Suppose the equation of the line is y = mx + c. (0,-1) is on this line so -1 = m*0 + c ie -1 = c so y = mx - 1 Also, (2,3) is on the line so 3 = m*2 - 1 or 2m = 4 so m = 2 So the equation of the line is y = 2x - 1