Write an equation passing through the point (-4,-1) and perpendicular to the line y = 2x - 4

Hello.

Perpendicular lines have slopes that are opposite reciprocals.

This means we take the slope of the given line, flop it over, and change its sign.

The slope of the given line is 2.

First, we flop it over:

Change its sign:

Now, we also have a point that the line passes through, so we can write its equation in Point-Slope Form:

Plug in the values:

(This is our final answer)

I hope it helps.

Have a nice day.

The point-slope form of the equation of line it's y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is the point the line passing through.

The slope-intercept form of the equation of line it's y = mx + b, where m is the slope and b is the y-intercept of the line.

1. Write the equation of the line that is parallel to y = 2x + 4 and passes through the point (-4, -1).

y=m₁x+b₁   ║   y=m₂x+b₂   ⇔    m₁ = m₂

{Two lines are parallel if  their slopes are equal}

y = 2x + 4  ⇒   m₁ = 2    ⇒    m₂ = 2

(-4, -1)  ⇒  x₁ = -4,  y₁ = -1

point-slope form:

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

y + 1 = 2(x + 4)

y + 1 = 2x + 8               {subtact 1 from both sides}

2. Write the equation of the line that is parallel to y = ⅓x - 3 and passes through the point (3, -1).

y = ⅓x - 3  ⇒   m₁ =  ⅓    ⇒    m₂ =  ⅓

(3, -1)  ⇒  x₁ = 3,  y₁ = -1

point-slope form:

y - (-1) = ⅓(x - 3)

y + 1 = ⅓x - 1           {subtact 1 from both sides}

3. Write the equation of the line that is perpendicular to y = ¾x - 1 and passes through the point (3, -3).

y=m₁x+b₁   ⊥   y=m₂x+b₂   ⇔    m₁×m₂ = -1

{Two lines are perpendicular if the product of theirs slopes is equal -1}

y = ¾x - 1   ⇒   m₁ = ¾  

¾×m₂ = -1        ⇒    m₂ = -⁴/₃

(3, -3)  ⇒  x₁ = 3,  y₁ = -3

point-slope form:

y - (-3) =  -⁴/₃(x - 3)

y + 3 = -⁴/₃x + 4           {subtact 3 from both sides}

4. Write the equation of the line that is perpendicular to y = -x - 5 and passes through the point (7, 3).

y = - x - 5   ⇒   m₁ = -1  

-1×m₂ = -1        ⇒    m₂ = 1

(7, 3)  ⇒  x₁ = 7,  y₁ = 3

point-slope form:

y - 3 =  -1(x - 7)

y - 3 = - x + 7           {add 3 to both sides}

y=1/2t+1

Step-by-step explanation:

To get a perpendicular line, the slopes have to be reciprocals.

y=1/2t+1

Step-by-step explanation:

To get a perpendicular line, the slopes have to be reciprocals.

x = 19/2

Step-by-step explanation:

The slopes of perpendicular lines have a product of -1.

Slope of line that passes through (4, 8) and (2, -1):

m1 = slope = (-1 - 8)/(2 - 4) = -9/(-2) = 9/2

Slope of perpendicular line is m2:

(m1)(m2) = -1

m2 = -1/m1 = -1/(9/2) = -2/9

The slope of the perpendicular line is -2/9

Now we write the expression for the slope of the second line. We use x for the unknown x-coordinate and -2/9 for the slope.

m2 = (5 - 2)/(-4 - x) = -2/9

3/(-4 - x) = -2/9

Cross multiply:

-2(-4 - x) = 3 * 9

8 + 2x = 27

2x = 19

x = 19/2

x = 19/2

Step-by-step explanation:

The slopes of perpendicular lines have a product of -1.

Slope of line that passes through (4, 8) and (2, -1):

m1 = slope = (-1 - 8)/(2 - 4) = -9/(-2) = 9/2

Slope of perpendicular line is m2:

(m1)(m2) = -1

m2 = -1/m1 = -1/(9/2) = -2/9

The slope of the perpendicular line is -2/9

Now we write the expression for the slope of the second line. We use x for the unknown x-coordinate and -2/9 for the slope.

m2 = (5 - 2)/(-4 - x) = -2/9

3/(-4 - x) = -2/9

Cross multiply:

-2(-4 - x) = 3 * 9

8 + 2x = 27

2x = 19

x = 19/2

See attached

Step-by-step explanation:

Both of the lines are drawn on the attached

A. .........................

Since lines AB and MY are parallel, and one of the points of parallel line is (-4, -1) the other point is going to have same difference of x and y-coordinates

Connecting this two points, we get a parallel line to AB

This is a blue line segment on the graph

B. .........................

Perpendicular lines have slopes of negative reciprocal

Considering this and one of the points of a perpendicular line of (-3, 4)

we can calculate the other point.

The other point will have coordinates:

and

So the line segment is QU with coordinates of (-3, 4) and (-1, -1)

This is red line segment on the graph

See attached

Step-by-step explanation:

Both of the lines are drawn on the attached

A. .........................

Since lines AB and MY are parallel, and one of the points of parallel line is (-4, -1) the other point is going to have same difference of x and y-coordinates

Connecting this two points, we get a parallel line to AB

This is a blue line segment on the graph

B. .........................

Perpendicular lines have slopes of negative reciprocal

Considering this and one of the points of a perpendicular line of (-3, 4)

we can calculate the other point.

The other point will have coordinates:

and

So the line segment is QU with coordinates of (-3, 4) and (-1, -1)

This is red line segment on the graph

a) y =2/3 x + 7.

b) x = -1

c) y = -4/5 x - 1/5

d) y = -3/2 x + 5/2.

Step-by-step explanation:

a) Intercept form y = mx + b where m = 2/3 and  b = 7

b) y can take any value but x is always -1.

c) Slope m = (-1-3)/ (1 - -4)

= -4/5

Using point-slope form where m = -4/5 and x1 y1 = 1 , -1:

y - y1 = m(x - x1)

y - -1 = -4/5(x - 1)

y + 1 = -4/5x + 4/5

y = -4/5 x - 1/5

d)  The slope m of the line perpendicular to this line is:

-1 / 2/3

m = -3/2.

When x = -1 , y = 4 so using the slope intercept form of a line

y = mx + b

4 = -3/2 * -1 + b  where b = the y-intercept.

4 = 3/2 + b

b = 4 - 3/2 = 5/2.

The equation is  y = -3/2 x + 5/2.

a) y =2/3 x + 7.

b) x = -1

c) y = -4/5 x - 1/5

d) y = -3/2 x + 5/2.

Step-by-step explanation:

a) Intercept form y = mx + b where m = 2/3 and  b = 7

b) y can take any value but x is always -1.

c) Slope m = (-1-3)/ (1 - -4)

= -4/5

Using point-slope form where m = -4/5 and x1 y1 = 1 , -1:

y - y1 = m(x - x1)

y - -1 = -4/5(x - 1)

y + 1 = -4/5x + 4/5

y = -4/5 x - 1/5

d)  The slope m of the line perpendicular to this line is:

-1 / 2/3

m = -3/2.

When x = -1 , y = 4 so using the slope intercept form of a line

y = mx + b

4 = -3/2 * -1 + b  where b = the y-intercept.

4 = 3/2 + b

b = 4 - 3/2 = 5/2.

The equation is  y = -3/2 x + 5/2.