Question

the city map project
a city planner has come to your office to ask for your help to map a new city. she knows lots of information about the
city, but she does not have a good map of all its streets and important landmarks. please follow her directions to create
a map of the city.
label all streets and landmarks! mark landmarks with icons, also.

1. start by creating a coordinate plane with an x and y axis. numbering is optional, but recommended.

(you might want to draw this lightly on the map)

1. name your new city

put this name at the top of your map.

1. the main street in your city is called equations ave. the equation of this street is y = 2x + 5

graph and label this street.

1. the next street in your city is called distributive blvd. the equation of this street is 3y = 2x - 9

wait! this equation is not in y = mx + b format! show your work as you transform the equation.
graph and label this street.

1. the next street in your city is called addition ave. the equation of this street is 3y + 45 = -4x

wait! this equation is not in y = mx + b format! show your work as you transform the equation.
graph and label this street.

1. the next street in your city is called numerator way the equation of this street is 2y - 22 = x

wait! this equation is not in y = mx + b format! show your work as you transform the equation.
graph and label this street.

1. the next street in your city is called denominator st. the equation of this street is x + y = 2

wait! this equation is not in y = mx + b format! show your work as you transform the equation.
graph and label this street.

1. there are also important landmarks in your city. plot and label the following:

triangle tower (6, -2) function fountain (-4, 14) pemdas point (10, 8) inverse place (-9, 1)
draw a symbol / icon for each of the landmarks, above.

1. parallel ave. is a street in the city. the planner doesnt know the equation of the street.

but, she knows that it is parallel to equations ave. and has a y-intercept of -12.
show your work as you write the equation for parallel ave in y = mx + b format
graph and label this street.

1. horizontal blvd. is a horizontal street with a y-intercept of -7 write the equation here:

graph and label this street.

1. vertical st. is a vertical street with an x-intercept of -8 write the equation here:

graph and label this street.

1. intersection circle is located at the coordinate where four streets intersect. what is this point? ( , )

draw a symbol / icon for this point

1. the fraction flower garden is at the corner of numerator and denominator what is this point? ( , )

draw a symbol / icon for this point

1. slope school is at the corner of equation and denominator what is this point? ( , )

draw a symbol / icon for this point

1. draw a compass rose to show north, south, east and west!

Explanation:

Step1: Analyze the problem type

This problem involves graphing linear equations, converting equations to slope - intercept form (\(y = mx + b\)), finding intersections of lines, and dealing with parallel lines. These are all concepts from Algebra (a sub - field of Mathematics).

Step2: For example, let's take part 4 (Distributive Blvd)

Step 2.1: Transform the equation

The equation is \(3y=2x - 9\). To get it into \(y=mx + b\) form, we divide both sides by 3.
\(y=\frac{2}{3}x-3\) (by the division property of equality, dividing each term in \(3y = 2x-9\) by 3: \(\frac{3y}{3}=\frac{2x}{3}-\frac{9}{3}\))

Step3: For part 9 (Parallel Ave)

Step 3.1: Recall the slope of parallel lines

Parallel lines have the same slope. The equation of Equations Ave is \(y = 2x+5\), so its slope \(m = 2\).

Step 3.2: Use the y - intercept

We know the y - intercept \(b=- 12\). Using the slope - intercept form \(y=mx + b\), the equation of Parallel Ave is \(y = 2x-12\).

Step4: For part 10 (Horizontal Blvd)

Step 4.1: Recall the equation of a horizontal line

A horizontal line has a slope \(m = 0\). The slope - intercept form is \(y=mx + b\). Since the y - intercept \(b=-7\) and \(m = 0\), the equation is \(y=-7\) (because \(y=0\times x-7=-7\)).

Step5: For part 11 (Vertical St)

Step 5.1: Recall the equation of a vertical line

A vertical line has an undefined slope and its equation is of the form \(x = a\), where \(a\) is the x - intercept. Since the x - intercept is \(-8\), the equation is \(x=-8\).

Step6: For finding intersections (e.g., part 13: Fraction Flower Garden at the corner of Numerator Way and Denominator St)

Step 6.1: Find the equations of Numerator Way and Denominator St

• Numerator Way: Start with \(2y-22=x\), transform to \(y=\frac{1}{2}x + 11\) (add 22 to both sides: \(2y=x + 22\), then divide by 2: \(y=\frac{1}{2}x+11\))
• Denominator St: Start with \(x + y=2\), transform to \(y=-x + 2\) (subtract \(x\) from both sides: \(y=-x + 2\))

Step 6.2: Solve the system of equations

Set \(\frac{1}{2}x + 11=-x + 2\)
Add \(x\) to both sides: \(\frac{1}{2}x+x+11=-x+x + 2\)
\(\frac{3}{2}x+11 = 2\)
Subtract 11 from both sides: \(\frac{3}{2}x=2 - 11=-9\)
Multiply both sides by \(\frac{2}{3}\): \(x=-9\times\frac{2}{3}=-6\)
Substitute \(x = - 6\) into \(y=-x + 2\): \(y=-(-6)+2=6 + 2=8\)
So the intersection point is \((-6,8)\)

(Note: This is just a sample of how to solve parts of the problem. The full solution would involve solving each part step - by - step as above, graphing the lines on the coordinate plane, plotting the landmarks, etc.)

Answer:

This problem is solved using concepts from Algebra (Mathematics). The solutions to individual parts are as follows (for example):

• 4. Equation of Distributive Blvd: \(y=\frac{2}{3}x - 3\)
• 9. Equation of Parallel Ave: \(y = 2x-12\)
• 10. Equation of Horizontal Blvd: \(y=-7\)
• 11. Equation of Vertical St: \(x=-8\)
• 13. Intersection of Numerator Way and Denominator St: \((-6,8)\)

(The full answer would include all the steps for graphing, labeling, and solving each part of the city map project as per the instructions.)