Let's break down the problem step by step to find the equation of the parallel street.

1. Find the slope of the given street: The given street passes through the points $(4, 7)$ and $(3, 3)$. The slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is calculated using the slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the coordinates of the points: $m = \frac{3 - 7}{3 - 4} = \frac{-4}{-1} = 4$ So, the slope of the given street is $4$.

2. Equation of the parallel street: Since parallel lines have the same slope, the parallel street will also have a slope of $4$. The equation of the line is in the form: $y = mx + b$ where $m = 4$ and $b$ is the y-intercept, which we need to find.

3. Find the y-intercept: The parallel street passes through the point $(-2, 4)$. Substitute $(-2, 4)$ and $m = 4$ into the equation $y = 4x + b$: $4 = 4(-2) + b$ Simplifying: $4 = -8 + b$ Solving for $b$: $b = 4 + 8 = 12$

4. Final equation: The equation of the parallel street is: $y = 4x + 12$

So, the correct answer is the first option: $y = 4x + 12$.

Do you want further details or have any questions?

Here are 5 questions to expand on this topic:

1. How do you find the slope of a line given two points?
2. What is the significance of the slope for parallel lines?
3. How do you use a point to find the y-intercept of a line?
4. Can two lines be parallel if their slopes are different?
5. How do you graph a linear equation on a coordinate plane?

Tip: When determining whether lines are parallel, always compare their slopes. Parallel lines will always have equal slopes!