Question

Line L passes through the points (0 - 3) and (6,9).
(a) Find the equation of line L.

(b) Find the equation of the line that is perpendicular to line L and passes through the point (0.2).

Answer 1

a)  find the slope of the line using the given points.

Slope:  9 - -3/6-0 then slope is 12/6 which is 2

Then using formula:  y = mx+b

-3 = 2(0) + b

b = -3

The equation is:  y = 2x -3

B. Slope of a perpendicular is -reciprocal of first line. So here the slope will be -1/2

y = mx + b is used again

2 = -1/2(0) + b

b = 2

The equation is:  y = -1/2x +2

Answer 2

The equation of line L passes through the points (0 - 3) and (6,9) is

y = 2x - 3

The equation of a line that is perpendicular to line L and passes through the point (0.2) is 2y + x = 4

The standard formula for finding the equation of a line is expressed as:

$y = mx + b$

m is the slope of the line

b is the y-intercept

Get the slope of the line:

$m=\frac{y_2-y_1}{x_2-x_1} \\m=\frac{9+3}{6-0}\\m=\frac{12}{6} \\m = 2$

The y-intercept of the line is -3

Get the equation of a line:

y = mx + b

y = 2x - 3

Hence the equation of line L passes through the points (0 - 3) and (6,9) is

y = 2x - 3

The equation of the line perpendicular to the line L has a slope of -1/2

The equation of the line that is perpendicular to line L and passes through the point (0, 2) is y - 2 = -1/2(x-0)

y - 2 = -1/2x

2(y - 2) = -x

2y - 4 = -x

2y + x = 4

Hence the equation of a line that is perpendicular to line L and passes through the point (0.2) is 2y + x = 4

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