Find the distance between the pair of parallel lines. y = 2x + 4, y = 2x - 3
a) 3.13
b) 3.20
c) 3.39
d) 3.56

The distance between the pair of given parallel lines is;

A: 3.13

We are given equation of the two lines as;

y = 2x + 4 - - - (eq 1)

y = 2x - 3 - - - (eq 2)

Let us put 1 for x in eq 1 to get;

y = 2(1) + 4

y = 6

Ax + By + C = 0

We have;

2x - y - 3 = 0

Thus;

A = 2

B = -1

C = -3

D = |Ax1 + By1 + c|/√(A² + B²)

Where;

x1 is the value of x imputed into the first equation

y1 is Tha value of y gotten from the input of x1

Thus;

D = |(2 × 1) + (-1 × 6) + (-3)|/(√(2² + (-1²))

D = |-7|/√5

We will take the absolute value of the numerator to get;

D = 7/√5

D = 3.13

Read more about distance between lines at;link

3.13

Step-by-step explanation:

Given :

y = 2x + 4 eq1

y = 2x - 3 eq2

sanity check : both equations have same slope, so we can conclude that they are both parallel to one another.

Step 1: consider equation 1, pick any random x-value and find they corresponding y-value. we pick x = -2

This gives us y = 2(-2) + 4 = 0

Hence we get a point (x,y) = (-2,0)

Step 2: express equation 2 in general form (i.e Ax + By + C = 0)

y = 2x-3 rearrange---> 2x - y -3 = 0

Comparing with the general form, we get A = 2, B = -1, C = -3

Recall that the distance between 2 parallel lines is given by the attached formula (see attached picture).

substituting the values for A, B, C and (x, y) from the previous step:

d = | (2)(-2) + (-1)(0) + (-3) |  / √(2² + (-1)²)

d = | -4 + 0 - 3 |  / √(4 + 1)

d = | -7 |  / √5

d = 7  / √5

d = 3.13

f

step-by-step explanation:

f

x/3-10=8

x/3=18

x=48