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
Anastasy [175]
1 year ago
12

Find the equation of the line that passes through (0, -3) and is parallel to

Mathematics
2 answers:
Tresset [83]1 year ago
8 0

Hey there!

\\

  • Answer:

\green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}}

\\

  • Explanation:

To find the equation of a line, we first have to determine its slope knowing that parallel lines have the same slope.

Let the line that we are trying to determine its equation be \: \sf{d_1} \: and the line that is parallel to \: \sf{d_1} \: be \: \sf{d_2} \: .

\sf{d_2} \: passes through the points (9 , 2) and (3 , -5) which means that we can find its slope using the slope formula:

\sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{y_2} - \orange{y_1}}{\red{x_2} - \blue{x_1 }}}

\\

⇒Subtitute the values :

\sf{(\overbrace{\blue{9}}^{\blue{x_1}}\: , \: \overbrace{\orange{2}}^{\orange{y_1}}) \: \: and \: \: (\overbrace{\red{3}}^{\red{x_2}} \: , \: \overbrace{\green{-5}}^{\green{y_2}} )}

\implies \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{-5} - \orange{2}}{\red{ \: \: 3} - \blue{9 }} = \dfrac{ - 7}{ - 6} = \boxed{ \bold{\dfrac{7}{6} }}}

\sf{\bold{The \: slope \: of \: both \: lines \: is \: \dfrac{7}{6}}}.

Assuming that we want to get the equation in Slope-Intercept Form, let's substitute m = 7/6:

Slope-Intercept Form:

\sf{y = mx + b} \\ \sf{Where \: m \: is \: the \: slope \: of \:  the \: line \: and \: b \: is \: the \: y-intercept.}

\implies \sf{y = \bold{\dfrac{7}{6}}x + b} \\

We know that the coordinates of the point (0 , -3) verify the equation since it is on the line \: \sf{d_1} \:. Now, replace y with -3 and x with 0:

\implies \sf{\overbrace{-3}^{y} = \dfrac{7}{8} \times \overbrace{0}^{x} + b} \\ \\ \implies \sf{-3 = 0 + b} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \sf{\boxed{\bold{b = -3}} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:

Therefore, the equation of the line \: \bold{d_1} \: is \green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}}

\\

▪️Learn more about finding the equation of a line that is parallel to another one here:

↣brainly.com/question/27497166

gayaneshka [121]1 year ago
4 0

Answer:

y = \frac{7}{6} x - 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \frac{y_{2}-y_{1}  }{x_{2}-x_{1}  }

with (x₁, y₁ ) = (9, 2 ) and (x₂, y₂ ) = (3, - 5 )

m = \frac{-5-2}{3-9} = \frac{-7}{-6} = \frac{7}{6}

• Parallel lines have equal slopes , so

m = \frac{7}{6} is the slope of the parallel line

the line crosses the y- axis at (0, - 3 ) ⇒ c = - 3

y = \frac{7}{6} x - 3 ← equation of parallel line

You might be interested in
What is the value of x? (giving brainliest and thanks to all!)
astra-53 [7]

Answer:

x° = 64°

Explaination:

This is a right angled triangle so one of the angle is 90°.

So, x° + 90° = 154° (Exterior angle property)

x° = 154° - 90° = 64°

Therefore x° = 64°

4 0
3 years ago
Samuel is trying to construct the inscribed circle of a triangle.
Yuki888 [10]

The next step to complete the construction will connect the in-center to one of the sides of the triangle.

<h3>What is a circle?</h3>

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

Samuel is trying to construct the inscribed circle of a triangle.

Using the angle bisectors to find the in-center.

Where two angles bisector meets, the point called in-center.

Next step will be: connect the in-center to one of the sides of the triangle.

Thus, the next step to complete the construction will be connect the in-center to one of the sides of the triangle.

Learn more about circle here:

brainly.com/question/11833983

#SPJ1

3 0
2 years ago
What is the scientific notation for 140000
vampirchik [111]
You move the decimal point forward until it reaches the one so it looks like this:

1.4 x 10⁵ 

the exponent, 5, just tells you how many spaces the decimal point moved.
6 0
3 years ago
Write the ratio as a fraction in simplest form a/b. What is the ratio of baseballs to basketballs?
Olin [163]
The ratio of baseballs to basketballs is

baseball: basketballs, or 

baseballs/basketballs

if you give me the numbers i can plug it in


hope this helps
7 0
3 years ago
How do I prove that a quadrilateral is a rectangle? (in a Column chart with statement and reason)
klasskru [66]
By definition, we have to:

 In plane geometry, a rectangle is a parallelogram whose four sides are at right angles to each other. Opposite sides have the same length.

 There is a proof that a quadrilateral is a rectangle:

  1) Its parallel sides are the same.

 2) Its two diagonals are the same, and they bisect each other at the common midpoint

 3) Any rectangle can be inscribed in a circle, two of whose diameters coincide with the diagonals of the rectangle.

 4) If all the angles of a quadrilateral are right angles, then it is a rectangle
7 0
3 years ago
Other questions:
  • HELLPP ME PLZZ. John goes to work by car or by train. The probability that John goes by car is 0.4. Work out the probability he
    8·1 answer
  • Two parallel lines are intersected by a transversal. Prove: Angle bisectors of the same side interior angles are perpendicular.
    12·1 answer
  • Make x the subject of the formula (mx^2=f)
    13·1 answer
  • Evaluate x+y when x=13 and y=−74. Write your answer as a fractionin simplest form
    10·1 answer
  • Evaluate the expression 3⋅f(−4)−3⋅g(−2)
    13·1 answer
  • Find the first five terms of the sequence defined below, where n represents the position of a
    5·1 answer
  • The Russian ruble coin has a radius of 10.25 mm. What is the circumference in terms of Pi?
    15·2 answers
  • Which inequalities are true? Select the four correct answers.
    6·1 answer
  • Pls answer ASAP
    13·1 answer
  • Find the shortest length of 1/2-inch conduit from which the following pieces can be cut: 7 1/8 inches, 3 1/4 inches, 6 1/2 inche
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!