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
GuDViN [60]
3 years ago
7

A line contains the points (-3, 4) and (7, -1). Calculate the equation of the line in the form y = mx + b Explain each step.

Mathematics
2 answers:
andre [41]3 years ago
6 0

\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{-1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-4}{7-(-3)}\implies \cfrac{-5}{7+3}\implies \cfrac{-5}{10}\implies -\cfrac{1}{2}

\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-4=-\cfrac{1}{2}[x-(-3)]\implies y-4=-\cfrac{1}{2}(x+3) \\\\\\ y-4=-\cfrac{1}{2}x-\cfrac{3}{2}\implies y=-\cfrac{1}{2}x-\cfrac{3}{2}+4\implies y=-\cfrac{1}{2}x+\cfrac{5}{2}

Daniel [21]3 years ago
3 0
In order to find the equation of the line, you must first find the gradient of the line

Gradient of a line (m)= (y2-y1)/(x2-x1)
.....Now you substitute the points...
= ((-1)-4)/(7-(-3))
= (-5)/(10)
= -1/2

Therefore the gradient is negative a half (-1/2)

Now we can find the equation of the line. You can use one of the two points to find the equation of the line

Equation of a line: y-y1=m(x-x1)
... I chose to use (7,-1) as my points....
y-(-1)=-1/2(x-7)
y+1=-x/2+7/2
y=-x/2+(7/2)-1
1) y=-x/2+5/2
..... if you would like you can multiply everything by 2 to have while numbers instead of fractions ....
2) 2y=-x+5
... if you are uncomfortable of having x as negative, you can transpose it carrying both the -x and the 5 to the side of the 2y. NOTE that the sign changes and the equation will be equal to 0....
3) 2y+x-5=0

1,2 and 3 are all correct answers, just in different forms

You might be interested in
Y>2x y>3 orderd pair
Ipatiy [6.2K]
<h2>Answer:</h2>

<h2>Step-by-step Explanation;</h2>

y  > 2x \: y \:  >  \: 3 \:  \\ solve \: for \: x \\ x \: € \: ( \frac{3}{2y}  \:  \frac{1}{2}  )\: y >  \: 3 \\ solve \: for \: y \\ y \:  >  \:  \frac{3}{2x}  \: x \:  >  \: 0 \: and \: x \:  < \:  \frac{1}{2}

<h2 />

<h2>HOPE IT HELPS!!!</h2>

<h2>I NEED BRAINLIEST ✌️</h2>
6 0
3 years ago
Help please, I don’t understand this
Solnce55 [7]

Answer:

r(14) = 29

Step-by-step explanation:

r(x) = 3/2x+8

r(14) = 3/2*14+8 = 21+8 = 29

6 0
3 years ago
Read 2 more answers
Please answer these 2 questions please!
Leno4ka [110]

Answer:

The 4th answer, at the bottom.

Step-by-step explanation:

The first answer is proportional, because y is equivalent to .5x.

The second answer is also proportional, because the ratios are equivalent.

The third answer is also proportional, because the line goes through the origin.

The fourth answer isn't proportional, because the ratios aren't equivalent.

5 0
3 years ago
A clerk is marking up merchandise 34%. The original price of an item is $455. What will be the retail price?
Galina-37 [17]
Take the orginal price and multiply it by 1.34.
455 * 1.34 = $609.70 in retail.

The longer way would be to take 34% of 455 and then add it to 455.

4 0
3 years ago
7) 2x + y = 7<br> What is the intercept
posledela

Answer:

2x + y = 7

x=7/2

y=7

Step-by-step explanation:

to find y itercept =0

to find x intercept=0

5 0
3 years ago
Other questions:
  • A light bulb consumes 3600 watt-hours per day. How long does it take to consume 18900 watt-hours?
    15·2 answers
  • X^2-4x-11=0 completing the square
    10·2 answers
  • (2x^3+4x^2-3)+(6x^3+4x-4)<br>​
    10·2 answers
  • 9000000 in standard form
    5·1 answer
  • Please help on this one?
    15·1 answer
  • Write the following as an expression or equation <br> 10 less than the product of a number and four
    6·1 answer
  • At Faith’s Fabulous Flowers, she uses 3 dozen roses in her “perfect day” bouquet. If she charges $39.99 for the entire bouquet,
    5·2 answers
  • A manufacturer of breakfast cereals is considering the following two designs for cereal boxes.
    14·2 answers
  • QUICK! heres the question. select the equations where x=3 is a soultion
    5·1 answer
  • The perimeter of the figure below is 64 m. Find the length of the missing side.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!