Question

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

Answer 1

Answer:

$y=-9x-4$

Step-by-step 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:

$m=-\frac{1}{n}$

For the line $y =\frac{1}{9}x+2$ the slope is: $m=\frac{1}{9}$

So the slope of the perpendicular line is:

$m=-\frac{1}{\frac{1}{9}}$

$m=-9$

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

Answer:

y=-9x-4

Step-by-step 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