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Through (-1,5) , perp to y =1/9x+2 write the slope intercept form for the equation

2 Answers

7 votes

Answer:


y=-9x-4

Explanation:

The equation of a line has the following form:


y=mx+b

Where m is the slope of the line and b is the intercept with the y axis.

If two lines of slopes m and n are perpendicular then it is true that:


m=-(1)/(n)

For the line
y =(1)/(9)x+2 the slope is:
m=(1)/(9)

So the slope of the perpendicular line is:


m=-(1)/((1)/(9))


m=-9

So the equation is:


y=-9x+b

To find b we substitute the point in the equation and solve for b


5=-9(-1)+b


b=5-9


b=-4

Then the equation of the line in the form of pending interception is:


y=-9x-4

User DanRedux
by
7.3k points
3 votes

Answer:

y=-9x-4

Explanation:

Perpendicular lines meet the following condition:

m2*m1= -1 (a)

where m is the slope of a line

m1 is given through equation of line 1, y =1/9 x+2

m2 must be -9 -> from eq. (a)

The Line has the following equation: y=mx+b, where m=-9 and the b is the interception with y axis.

Evaluating the above equation in (-1,5) we have the following equation

5= -9*(-1)+b, we have b=-4

The line has the following equation

y=-9x-4

Slope intercept form

User PMC
by
7.5k points