Perpendicular to the line

Question

Find the equation of the line with the given properties. Express the equation in general form or slope-intercept form.
Perpendicular to the line 10x + y = 107: contains the points (10,6)

The equation of the line is ___________

 

Type an equation. Type your answer in general form or slope-intercept form

Answer 1

The slopes of perpendicular lines are negative reciprocals. First, we need to find the slope of the original line. The slope intercept form of a line is y=mx+b where x & y are any coordinates on the line, m is the slope and b is the y-intercept. Let's put the original equation into this form:   10x+y=107     original equation

                                                                    y=-10x+107   slope intercept form

From here we can see that the original slope is -10. The negative reciprocal of this is -(-1/10)=1/10. Now we know the slope of the perpendicular line. So, now what we have is  y=(1/10)x+b. Use the point, (10,6), to find b:

                                             y=(1/10)x+b

                                             6=(1/10)(10)+b

                                             6=1+b

                                             b=5

We now have the slope and the y-intercept of the perpendicular line. Just put these values into the slope intersept of a line:                                      y=mx+b               slope intercept form of a line

                                            y=(1/10)x+5         substitute for m & b

We usually don't like to leave anything in fractions, so multiply everything by 10 to get rid of the fraction:

                                            y=(1/10)x+5         new equation

                                            10y=x+50             everything multiplied by 10

                                            0=x-10y+50 or x-10y=-50 general form of a line.        

Answer 2

y = 107 - 10x

 

M= 1/10

 

B = y - mx = 6 - (1/10)(10) = 6 - 1 = 5

 

y = (1/10)x + 5