Answered

A design engineer is mapping out a new neighborhood with parallel streets. If one street passes through (4, 7) and (3, 3), what is the equation for a parallel street that passes through (−2, 4)?

y = 4x + 12
y = 4x − 14
y equals negative one-fourth times x minus 1
y equals negative one-fourth times x plus 7 halves

Answer :

Answer:

Step-by-step explanation:

The Answer is A

The equation for a parallel street that passes through the given point is y = 4x + 12

Equation of a line

From the question, we are to determine the equation of the street that is parallel to the first street

NOTE: Two lines are parallel if they have equal slopes.

Thus,

We will determine the slope of the first street.

From the given information,

The street passes through the points (4, 7) and (3, 3)

Using the formula,

Slope = (y₂ - y₁)/(x₂ - x₁)

x₁ = 4

y₁ = 7

x₂ = 3

y₂ = 3

∴ Slope = (3 -7)/(3 -4)

Slope = -4/-1

Slope = 4

Now,

For the equation of the parallel street

The street passes through the point (-2, 4)

Since, the street is parallel to the first street,

Slope = 4

Using the point-slope form

y - y₁ = m(x - x₁)

y - 4 = 4(x - -2)

y - 4 = 4(x + 2)

y - 4 = 4x + 8

y = 4x + 8 + 4

y = 4x + 12

Hence, the equation for a parallel street that passes through the given point is y = 4x + 12

Learn more on Equation of a line here: https://brainly.com/question/13763238

#SPJ1

Go Question: Other Questions