SOLUTION: Find in each case the value of k so that the line r: y = kx + 1 is: A) Parallel to the OX axis B) Perpendicular to the line 2x + 3y + 7 = 0

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Question 1071535: Find in each case the value of k so that the line r: y = kx + 1 is:
A) Parallel to the OX axis
B) Perpendicular to the line 2x + 3y + 7 = 0
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
if the line is parallel to the x-axis, then k must be equal to 0.

you will get y = 0x + 1 which becomes y = 1.

if the line is perpendicular to the line 2x + 3y + 7 = 0, then the slope of the line formed has to be the negative reciprocal of the slope of the original line.

put the original equation in slope intercept form.

start with:

2x + 3y + 7 = 0
subtrace 7 from both sides to get:
2x + 3y = -7
subtract 2x from both sides to get:
3y = -2x - 7
divide both sides by 3 to get:
y = -2/3 * x - 7/3

the slope of your original equation is -2/3.
the negative reciprocal of this is 3/2.
the slope of your line perpendicular to the orginal line is 3/2.

your equation of y = kx + 1 becomes:
y = 3/2 * x + 1

k is equal to 3/2.

here's the graph of your equations.

the red line is the equation y = 1.
this line is parallel to the x-axis.

the orange line is the equations:
y = -2/3 * x - 7/3 and 2x + 3y + 7 = 0
these equations are equivalent and therefore draw the same orange line.
they reprewsent the original equation.

the green line is the equation y = 3/2x + 1.
this line is perpendicular to the orange line.