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

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

Step-by-step explanation:

The equation of a line has the following form:

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:

For the line the slope is:

So the slope of the perpendicular line is:

So the equation is:

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

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

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is