Question

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

Answer 1

`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`

Answer 2

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