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
yulyashka [42]
2 years ago
6

Write an equation in slope-intercept form for the following line: (-17,-4) and (-7,-13)

Mathematics
1 answer:
Wittaler [7]2 years ago
7 0
<h2>Slope-intercept form</h2>

Linear equations are often organized in slope-intercept form:

y=mx+b

  • <em>(x,y)</em> = a point that falls on the line
  • <em>m</em> = the slope of the line
  • <em>b</em> = the y-intercept of the line

<h3>Slope (m)</h3>

The slope of a line is equal to its \dfrac{rise}{run}.

  • <em>"Rise"</em> refers to the number of units the line travels up.
  • <em>"Run"</em> refers to the number of units the line travels to the right.

Typically, we would solve for the slope by using the following formula:

  • m=\dfrac{y_2-y_1}{x_2-x_1} where two points that fall on the line are (x_1,y_1) and (x_2,y_2)

<h3>Y-intercept (b)</h3>

The y-intercept of a line refers to the y-value that occurs when x=0.

On a graph, it is the y-value where the line crosses the y-axis.

<h2>Writing the Equation</h2>

1) Determine the slope of the line (m)

m=\dfrac{y_2-y_1}{x_2-x_1}

Plug in the two given points, (-17,-4) and (-7,-13):

m=\dfrac{-13-(-4)}{(-7)-(-17)}\\\\m=\dfrac{-13+4}{-7+17}\\\\m=\dfrac{-9}{10}

Therefore, the slope of the line is -\dfrac{9}{10}. Plug this into y=mx+b:

y=-\dfrac{9}{10}x+b

2) Determining the y-intercept (b)

y=-\dfrac{9}{10}x+b

Plug in one of the given points and solve for b:

-4=-\dfrac{9}{10}(-17)+b\\\\-4=\dfrac{153}{10}+b\\\\b=-\dfrac{193}{10}

Therefore, the y-intercept of the line is -\dfrac{193}{10}. Plug this back into our equation:

y=-\dfrac{9}{10}x-\dfrac{193}{10}

<h2>Answer</h2>

y=-\dfrac{9}{10}x-\dfrac{193}{10}

You might be interested in
A store is having a 25•/• off sale on all shirts. show two ways to calculate the sale price for a shirt that normally costs $24.
tia_tia [17]
24 x .25 is 6, so 24 - 6 is $18.00.

I don't know another way sorry.
3 0
3 years ago
Read 2 more answers
Which expression does not belong with the other three? Explain your reasoning. 8 = x —2 3 = x ÷ 4 x − 6 = 5 x —3 = 9
Scorpion4ik [409]

Answer:

  • 3 = x ÷ 4

Step-by-step explanation:

<u>Given expressions:</u>

  • 8 = x - 2 ⇒ x = 8 + 2= 10
  • 3 = x ÷ 4  ⇒ x = 3*4 = 12
  • x - 6 = 5  ⇒ x = 5 + 6 = 11
  • x - 3 = 9  ⇒ x = 9 + 3 = 12

3 of them involves addition, one of them - multiplication

The second expression doesn't belong

4 0
3 years ago
USLUIT il<br> Find x.<br> 45°<br> 30°
IceJOKER [234]

Answer:

111°

Step-by-step explanation:

  • All these are parallel lines, so the 36° angle is equal to the 36° angle inside the big triangle because they are vertically opposite.

  • Ignore the line cutting between 45° and the 30° and consider it as one triangle
  • Add them to get 75°
  • Now you have two known angles 75° and 36°
  • To get angle <em>x</em><em> </em>add 75° and 36° to get 111°
  • Because x° is an exterior angle and exterior angles equal to the sum of interior angles opposite it inside the triangle.
7 0
3 years ago
19.
vichka [17]

Answer:

168

Step-by-step explanation:

Sum the parts of the ratio, 6 + 7 = 13 parts

Divide the total number of students by 13 to find the value of one part of the ratio.

364 ÷ 13 = 28 ← value of 1 part of the ratio, thus

number of girls = 6 × 28 = 168

3 0
3 years ago
What is the longest line segment that can be drawn in a right rectangular prism that is 14cm​ long, 13cm​ wide, and 11cm​ tall?
vlabodo [156]

The longest line segment that can be drawn in a right rectangular prism that is 14cm long, 13cm wide and 11cm tall is 19.1cm.

<h3>What is a right rectangular prism?</h3>

A right rectangular prism is a three dimensional solid shape formed by 6 rectangles.

it is also called the cuboid.

Analysis:

The diagonal of the face of the prism with dimensions 14cm long and 13cm wide is the longest line segment that can be drawn.

Since rectangles have 90° on each vertex, we can use Pythagoras theorem to calculate for the length of the diagonal.

(diagonal)^{2} = (length)^{2} + (width)^{2}

(diagonal)^{2} = (14)^{2} + (13)^{2}

                 = 196 + 169 = 365

 (diagonal)^{2} = 365

diagonal = \sqrt{365} = 19.1cm

In conclusion, the length of the longest diameter is 19.1cm

Learn more about Right rectangular prism: brainly.com/question/3317747

#SPJ1

               

4 0
1 year ago
Other questions:
  • Sam's bedroom has a perimeter of 46 feet. If the length of the bedroom is 11 feet, what is the width of the bedroom?
    10·1 answer
  • A triangle on a coordinate plane is translated according to the rule T-8,4(x,y). Which is another way to write this rule
    5·2 answers
  • How do you find the surface area of a cube?
    10·1 answer
  • How do you apply proportional reasoning
    13·1 answer
  • Which of the following is equivalent to 2^(2x+1)?
    10·1 answer
  • (4x²y³ + 2xy² – 2y) – (–7x²y³ + 6xy² – 2y)<br> Find the difference of polynomials ?
    14·1 answer
  • A thunderstorm travels at a constant speed. In 15 minutes , the storm travels 12 miles. If the storm continues to travel at the
    13·1 answer
  • Solve for x<br> B<br> 31°<br> С<br> 26<br> X=<br> (Round to the nearest hundredth.)
    12·1 answer
  • Can someone help me with this?
    6·2 answers
  • The table represents an exponential function. What is the multiplicative rate of change of the function? 07 1 2 un un 3 2 2 5 2
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!