What is the y-intercept of the line perpendicular to the line y = 3/4x+3 that includes the point (3, 1)?

The y-intercept is the point (0,5)

Step-by-step explanation:

step 1

Find the slope of the line perpendicular to the line y=(3/4)x+3

Remember that

If two lines are perpendicular, then the product of their slopes is equal to -1

m1*m2=-1

we have

m1=3/4 > the slope of the line y=(3/4)x+3

Find m2

substitute

(3/4)*m2=-1

m2=-4/3

step 2

Find the equation of the line into point slope form

The equation is equal to

y-y1=m(x-x1)

we have

m=-4/3

(x1,y1)=(3,1)

substitute

y-1=-(4/3)(x-3) > equation of the line into point slope form

step 3

Find the y-intercept

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

substitute in the equation of the line and solve for y

y-1=-(4/3)(0-3)

y-1=4

y=4+1=5

The y-intercept is the point (0,5)

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,