Mathematics : asked on LEXIEXO

28.12.2021

What is an equation of the line that passes through the points ( − 1 , − 2 )and ( − 2 , − 5 ) ?

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Step-by-step answer

09.07.2023, solved by verified expert

Mathematics, DAV Post Graduate College

5 229 answers

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y = 3x + 1

Step-by-step explanation:

You have to use y = m x + c to find the equation of the line.

Here,

m ⇒ slope

c ⇒ y - intercept

First let us find the slope by using the below formula.

For that, let us use the given coordinates.

( -1 , -2 ) ⇒ ( x₁ , y₁ )

(-2 , -5) ⇒ ( x₂ , y₂ )

m =

m =

m =

m =

m = 3

Now we have to find the y - intercept.

For that we can use any coordinate for that.

Let us use ( -1 , -2 ) coordinate.

y = m x + c

-2 = 3 × -1 + c

-2 = -3 + c

- 2 + 3 = c

1 = c

Let us write the equation of the line now.

y = m x + c

y = 3 x + 1

Let me know if you have any other questions. :-)

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Mathematics

What is an equation of the line that passes through the points ( − 1 , − 2 )and ( − 2 , − 5 ) ?

Step-by-step answer

P Answered by Master

y = 3x + 1

Step-by-step explanation:

You have to use y = m x + c to find the equation of the line.

Here,

m ⇒ slope

c ⇒ y - intercept

First let us find the slope by using the below formula.

For that, let us use the given coordinates.

( -1 , -2 ) ⇒ ( x₁ , y₁ )

(-2 , -5) ⇒ ( x₂ , y₂ )

m = $\frac{y_1-y_2}{x_1-x_2}$

m = $\frac{-2-(-5)}{-1-(-2)}$

m = $\frac{-2+5}{-1+2}$

m = $\frac{3}{1}$

m = 3

Now we have to find the y - intercept.

For that we can use any coordinate for that.

Let us use ( -1 , -2 ) coordinate.

y = m x + c

-2 = 3 × -1 + c

-2 = -3 + c

- 2 + 3 = c

1 = c

Let us write the equation of the line now.

y = m x + c

y = 3 x + 1

Let me know if you have any other questions. :-)

Mathematics

Ineed the answers to these questions quickly, : choose the equation of the line passing through the point (-4, -2)and parallel to y = 1/4 x + 2. y = 1/4 x - 1 y = 4x - 1 y = 1/4 x - 3 y = 4x - 3 choose the equation of the line passing through the point (-1, 7)and perpendicular to y = -1/4x - 5. y = 4x + 3 y = -4x - 11 y = -4x - 3 y = 4x + 11

Step-by-step answer

P Answered by PhD

y = 1/4 x - 1 y = 4x + 11

Step-by-step explanation:

It is probably easiest to identify the required slope so you can eliminate the bogus answers, then try the point in the remaining equations to see what works.

1. Parallel lines have the same slope. A line parallel to a line with slope 1/4 will also have slope 1/4, eliminating the 2nd and 4th answer choices.

Trying the point in the first answer choice, we have ...

-2 = (1/4)(-4) -1 . . . . true . . . . . y = 1/4x -1 is the correct equation

__

2. Perpendicular lines have slopes that are the negative reciprocal of each other. -1/(-1/4) = 4, eliminating the 2nd and 3rd choices.

Trying the point in the first answer choice, we have ...

7 = 4(-1) +3 . . . . . . false

The last answer choice gives ...

7 = 4(-1) +11 . . . . . . true . . . . . . y = 4x +11 is the correct equation

Mathematics

Ineed the answers to these questions quickly, : choose the equation of the line passing through the point (-4, -2)and parallel to y = 1/4 x + 2. y = 1/4 x - 1 y = 4x - 1 y = 1/4 x - 3 y = 4x - 3 choose the equation of the line passing through the point (-1, 7)and perpendicular to y = -1/4x - 5. y = 4x + 3 y = -4x - 11 y = -4x - 3 y = 4x + 11

Step-by-step answer

P Answered by PhD

y = 1/4 x - 1 y = 4x + 11

Step-by-step explanation:

It is probably easiest to identify the required slope so you can eliminate the bogus answers, then try the point in the remaining equations to see what works.

1. Parallel lines have the same slope. A line parallel to a line with slope 1/4 will also have slope 1/4, eliminating the 2nd and 4th answer choices.

Trying the point in the first answer choice, we have ...

-2 = (1/4)(-4) -1 . . . . true . . . . . y = 1/4x -1 is the correct equation

__

2. Perpendicular lines have slopes that are the negative reciprocal of each other. -1/(-1/4) = 4, eliminating the 2nd and 3rd choices.

Trying the point in the first answer choice, we have ...

7 = 4(-1) +3 . . . . . . false

The last answer choice gives ...

7 = 4(-1) +11 . . . . . . true . . . . . . y = 4x +11 is the correct equation

Mathematics

What is an equation of the line that passes through the points (-2, -3)and (-1, 2)? Put your answer in fully reduced form.

Step-by-step answer

P Answered by Specialist

1

y = 5x + 7

Step-by-step explanation:

In order to create the equation in slope-intercept form (y = mx + b) we'll need to find the slope and the y-intercept.

To find the slope, we can use this expression: $\frac{y2 - y1}{x2 - x1}$

First, input the points: $\frac{2 - (-3)}{-1 - (-2)}$

Solve: $\frac{5}{1}$

Simplify: $\frac{5}{1}$ = 5

Now we can input the value of the slope into the equation.

y = 5x + b

To find the y-intercept (b), we'll input one of the given points and solve for b.

Input the values of x and y from the given point (-1,3): 2 = 5(-1) + b

Simplify the right side of the equation: 2 = -5 + b

Add 5 to both sides to isolate the b: 7 = b

Now that we know both the slope and the y-intercept, we can put them into the equation and find our answer.

5 = slope 7 = y-intercept

y = 5x + 7

Mathematics

What is an equation of the line that passes through the points (-2, -5)and (-1, 1)?

Step-by-step answer

P Answered by PhD

3

y = 6x + 7

Step-by-step explanation:

We can use slope formula to find the slope of a line that passes through two points (x₁ , y₁) and (x₂ , y₂)

m = ∆y/∆x = y₂-y₁/x₂-x₁

Given points are: P(x₁ , y₁) = (-2, -5) and Q(x₂ , y₂) = (-1, 1)

Substituting these two known points in the slope formula, we have:

m = (1-(-5))/(-1-(-2)) = 1+5/-1+2 = 6/1 = 6

Now we can use the point-slope formula to write the equation of a line given a point on the line and the slope of the line:

m = 6 , given point P(x₁,y₁) = (-2, -5)

Formula = (y-y₁) = m(x-x₁)

(y-(-5)) = 6(x-(-2))

y+5 = 6x + 12

y = 6x + 12 -5

y = 6x + 7

y = 6x + 7

Spymore

StudenGPT

The line described by the equation −4x+y=2 is graphed on a coordinate plane. Which equation describes the graph of a line passing through the point (−1,3)and parallel to the line described by −4x+y=2

Step-by-step answer

P Answered by Studen AI

1

To find the equation of a line parallel to a given line, we need to understand that parallel lines have the same slope.

Let's analyze the given line's equation: -4x + y = 2.

To put this equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we need to isolate y.

Rearranging the equation, we get:
y = 4x + 2.

From this equation, we can determine that the slope of the given line is 4.

Now, we can use the slope-intercept form to find the equation of the line parallel to this line and passing through the point (-1, 3).

Using the point-slope form (y - y1 = m(x - x1)), where (x1, y1) are the coordinates of the given point and m is the slope, we have:
y - 3 = 4(x - (-1)).

Simplifying this equation, we get:
y - 3 = 4(x + 1).

Next, we distribute 4 into (x + 1):
y - 3 = 4x + 4.

To isolate y, we add 3 to both sides:
y = 4x + 7.

So, the equation of the line passing through (-1, 3) and parallel to the line -4x + y = 2 is y = 4x + 7.

Using math laws and steps, we followed the slope-intercept form and point-slope form to find the equation. We carefully canceled out terms, distributed negative signs, and combined like terms accurately. The final equation was verified by substituting (-1, 3) as a point on the line and checking if it satisfied the equation.

Mathematics

What is the slope of the line passing through the points (−1, 7)and (4, −1) −2 2 8/8 -5/6

Step-by-step answer

P Answered by Specialist

5

(-1,7)(4,-1) m=y2-y1/x2-x1

-1-7= -8
4-(-1)= 5

wouldnt the slope be -8/5?

Mathematics

Determine if lines passing through the points are parallel,perpendicular,or neither line 1: (-2,2)and (2,-4) line 2: (3,6) and (5,3)

Step-by-step answer

P Answered by Specialist

1

You can tell if two lines are parallel, perpendicular, or neither by looking at their slopes m_1 and m_2 :

If

m_1=m_2

, i.e. if the two lines have the same slope, the lines are parallelIf $m_1\cdot m_2=-1$ , the lines are perpendicularIn all other cases, the lines are not parallel nor perpendicular.

Given two points $A = (x_A,y_A),\ B = (x_B,y_B)$ of a line, the slope is defined as the ratio between the y and x variation:

$m = \dfrac{\Delta y}{\Delta x} = \dfrac{y_B-y_A}{x_B-x_A}$

So in this case, we have

$m_1 = \dfrac{2-(-4)}{-2-2} = \dfrac{6}{-4} = -\dfrac{3}{2}$

$m_2 = \dfrac{3-6}{5-3} = \dfrac{-3}{2} = -\dfrac{3}{2}$

Since the two slopes are the same, the two lines are parallel.

Mathematics

What is the slope of the line passing through the points (−1, 7)and (4, −1) −2 2 8/8 -5/6

Step-by-step answer

P Answered by Specialist

5

(-1,7)(4,-1) m=y2-y1/x2-x1

-1-7= -8
4-(-1)= 5

wouldnt the slope be -8/5?

Mathematics

Determine if lines passing through the points are parallel,perpendicular,or neither line 1: (-2,2)and (2,-4) line 2: (3,6) and (5,3)

Step-by-step answer

P Answered by Specialist

1

You can tell if two lines are parallel, perpendicular, or neither by looking at their slopes m_1 and m_2 :

If

m_1=m_2

, i.e. if the two lines have the same slope, the lines are parallelIf $m_1\cdot m_2=-1$ , the lines are perpendicularIn all other cases, the lines are not parallel nor perpendicular.

Given two points $A = (x_A,y_A),\ B = (x_B,y_B)$ of a line, the slope is defined as the ratio between the y and x variation:

$m = \dfrac{\Delta y}{\Delta x} = \dfrac{y_B-y_A}{x_B-x_A}$

So in this case, we have

$m_1 = \dfrac{2-(-4)}{-2-2} = \dfrac{6}{-4} = -\dfrac{3}{2}$

$m_2 = \dfrac{3-6}{5-3} = \dfrac{-3}{2} = -\dfrac{3}{2}$

Since the two slopes are the same, the two lines are parallel.

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