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

a. -5/4

b. 3

c. -13/4

d. 5

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:

hello :

the line perpendicular to the line y = 3/4x + 3 is : y = ax+b when : a×3/4=-1

so : a = -4/3

y = -4/3 x +b

now calculate b : this line passes by the point (3, 1) meanes :   1 = -4/3(3)+b

so b= 5   so : y = -4/3 x +5

the y-intercept for this line when x= 0   : y = -4/3(0)+5   y = 5

  D.  5

Step-by-step explanation:

The attached shows a graph of the line in point-slope form. It has a y-intercept of 5.

The slope of the given line is 3/4. The slope of the perpendicular line will be the negative reciprocal of that: -1/(3/4) = -4/3.

The point-slope form of the equation of a line with slope m through point (h, k) can be written ...

  y = m(x -h) +k

For the desired slope and given point, this equation is ...

  y = (-4/3)(x -3) +1 = (-4/3)x +4 +1

  y = (-4/3)x +5 . . . . . equation in slope-intercept form

The y-intercept is seen to be 5.