1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Tresset [83]
2 years ago
12

1. Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the

given equation. (1,-3; y + 2 – 4(x-1)
2. Are the graphs of the equations y = -2x +3 and 2x +y = 7, parallel, perpendicular, or neither? Explain.

3. A line passes through (5,0) and is perpendicular to the graph of y +1 = 2(x-3). What equation represents the line in slope-intercept form?

4. A bike path is being planned for the park. The bike path will be parallel to Main Street and will pass through the park entrance. What is an equation of the line that represents the bike path? (use image from Ex.4)

5. Determine whether this statement is always, sometimes, or never true. Two line with the same slope and different y-intercepts are perpendicular.

Mathematics
2 answers:
skelet666 [1.2K]2 years ago
8 0
1. the equation y + 2 = -4(x - 1) needs to be in slope-intercept form. it makes it easier to solve. first, distributive property. y + 2 = -4x + 4 now you can subtract 2 from both sides to isolate y. new equation: y = -4x + 2 now you can graph this equation and the point (1, -3). we know the slope of the equation has to be the same so we can go up 4 and 1 to the left from (1, -3). this new point is (0, 1). so the answer is: y = -4x + 1

2. the graphs of the equations y = -2x + 3 and y = -2x + 7 are parallel.
i changed 2x + y = 7 to y = -2x + 7 by subtracting 2 from both sides. (standard form to slope-intercept form) then, i determined they were parallel by graphing them. you can visually see they're parallel to each other.

3. y + 1 = 2(x - 3) <- standard form. to transform this into slope-intercept form, you have to start by using the distributive property. so, do 2 times x and 2 times -3. new equation: y + 1 = 2x - 6 now you add 6 to both sides. new equation: y + 7 = 2x all you have to do now is get this in slope-intercept form. to do this, just subtract 7 from both sides. new equation: y = 2x - 7

4. the bike path is going to be parallel to main street. it is also going to pass through the park entrance (0, 4). the equation of main street is y = 2x - 3
we know that the park entrance is (0, 4) so the equation is going to look like this so far: y = x + 4 we also know the slope of the equation of main street is 2x and for the bike path to be parallel the slope needs to be the same. therefore, the equation of the line that represents the bike path is y = 2x + 4.

5. the statement: two lines with the same slope and different y-intercepts are perpendicular. is never true. this is because two lines with the same slope and different y-intercepts are parallel, not perpendicular.

i know this is a lot to read, but i like explaining things just to make sure you understand everything. the answers are in bold. i hope this helps! 
Sveta_85 [38]2 years ago
3 0

Answer:

#1) y = -4x + 1; #2) parallel; #3) y = -1/2x + 5/2; #4) y = 2x + 4; #5) Never

Step-by-step explanation:

#1) We want a line that passes through (1, -3) and is parallel to y = 2-4(x-1).  First we simplify our equation using the distributive property:

y = 2-4(x-1) = 2-4(x) -4(-1) = 2-4x--4 = 2-4x + 4 = -4x + 6

Lines that are parallel have the same slope; this means we want a line through (1, -3) with a slope of -4.  Using point-slope form,

y-y_1=m(x-x_1)\\\\y--3=-4(x-1)\\\\y+3=-4(x)-4(-1)\\\\y+3=-4x+4\\\\y+3-3=-4x+4-3\\\\y=-4x+1

#2) We must first write our second equation in slope-intercept form by isolating the y term:

2x+y=7

Subtract 2x from each side"

2x+y-2x = 7-2x

y = -2x+7

This means the slope is -2; the slopes are the same, so the lines are parallel.

#3) The slope of our given equation is 2.  To be perpendicular, the second line must have a slope that is a negative reciprocal (flipped and opposite signs); this makes it -1/2.  Using point-slope form,

y-0=\frac{-1}{2}(x-5)\\\\y=\frac{-1}{2}(x)+\frac{-1}{2}(-5)\\\\y=\frac{-1}{2}x+\frac{5}{2}

#4) The slope of Main Street on the diagram, found by using rise/run, is 2.  This means the bike path will also have a slope of 2 in order to be parallel.  The park entrance is at (0, 4).  This makes the equation y = 2x+4.

#5) Two lines with the same slope are always parallel.  They are never perpendicular.

You might be interested in
the legs of a right triangle have lengths of 28 meters and 21 meters. the hypotenuse has a lenght of 5x meters. what is the valu
Luba_88 [7]
From the Pythagorean Theorem, we know that a^2+b^2=c^2
28^2+21^2=(5x)^2
784+441=25x^2
1225=25x^2
49=x^2
x=7
The length of the hypotenuse would be 35m.
7 0
3 years ago
Read 2 more answers
(8.4x + 2.9) + (-3.7x + 5).
konstantin123 [22]

Answer:

10

Step-by-step explanation:

4 0
3 years ago
QUESTION BELOW PLS HELP
Sidana [21]

Answer:

B. V-Vo/t

Step-by-step explanation:

All you have to do is redistribute the equation

3 0
3 years ago
the graph shows the equation x^2+y^2=5 use the slider for a to move the vertical line on the graph based on the vertical line te
SSSSS [86.1K]

Answer:

Not a function.

Step-by-step explanation:

The vertical line touches the graph at more than one point at once.

4 0
1 year ago
What is the answer to y divided by 2 = 17
bija089 [108]
The answer is Y=34
Because 34/17 is 34
7 0
2 years ago
Read 2 more answers
Other questions:
  • Jacob used 1/7 of a liter of water to fill 1/9 of the fish aquarium. How many liters r needed to fill the aquarium?
    10·2 answers
  • The volume of a sphere is 5000 pi meters cubed. What is the surface area
    6·1 answer
  • You check 20 cartons of eggs. Three of the cartons have at least one cracked egg. What is the experimental probability that a ca
    14·1 answer
  • Plz Help
    13·1 answer
  • Make a down payment of $1500 and finance the rest of $20000 at 1.9% interest rate, making equal monthly payments for 5 years.
    10·2 answers
  • Mrs. Walker is instructing a team of students on designing the sailboat shown. Beth is working on the smaller sail, which is a r
    10·2 answers
  • Please help me with this
    5·1 answer
  • Pls help. Find the surface area of the solid. Round to the nearest tenth if necessary
    10·1 answer
  • F(x)=x^2-9 how many roots in common
    8·1 answer
  • Which number is irrational?<br> OA. 0.45<br> OB. 0.636363...<br> O C. √25<br> OD. √6
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!