# Find the equation of the line of the form y=mx+b that passes through the following pair of points 1.(3,-1) (7,-5) 2.(2,3) (5,6) ,2) (4,2)

Answers: 3

## Answers

Find the equation of the line of the form y=mx+b that passes through the following pair of points 1....

5y=3x+11

Step-by-step explanation:

(3, 4), (-2, 1)

(x1, y1), (x2, y2)

SUBSTITUTE

(y-4) = 1-4/-2-3(x-3)

(y-4) = -3/-5(x-3)

(y-4) = 3/5(x-3)

(y-4) =3/5x - 9/5

y = 3/5x - 9/5 + 4

y = 3/5x + 11/5

(y = 3/5x + 11/5) 5

5y=3x+11Writing the equations of lines, however, requires the use of other forms depending on the given properties of the function:

1. THE SLOPE- INTERCEPT FORM- the linear function has been defined in terms of the equation f(x) = mx +b. this form is called the slope intercept form.

2. THE POINT- SLOPE FORM- IF the graph of linear function y has a slope m and passes through the point ( x₁, y₁ , then its equation is y - y1 = m (x - x1).

3. THE TWO –POINT FORM – if the graph of the linear function y passes through the point ( x₁, y₁) and (x₂, y₂), its equation according to the point – slope form is y - y₁ = m (x - x₁). But by its definition m = (y₂-y₁ )/(x₂-x₁) . By substitution y - y₁ = (y₂-y₁ )/(x₂-x₁) (x - x₁).

Read the details about slope and an example of slope in

Given: Find the equation of the line of the form y = mx + b that passes through the following pairs of points. 10. (- 5/2 , 3/2) and (1/2, -1/4)

STEPS: Substitute the values to the TWO- POINT FORM, then transform the resulting equation in the required form: SimplifySOLUTION:X₁ = -5/2, x₂ = 1/2

Y₁ = 3/2, y₂ = -1/4

y - y₁ = (y₂-y₁ )/(x₂-x₁) (x - x₁)

y- 3/2= ((-1/4-3/2)/(-1/2- -5/2) )( x - - 5/2)

y - 3/2 = ((-7/4/ 2))( x+5/2)

y -3/2 = -7/2(x +5/2)

y -3/2 = -7/2x - 35/4

y= -7/2x – 35/ 4 + 3/2

y= -7/2 x – 29/ 4

the equation is y= -7/2 x – 29/ 4Read the details about an example of slope and write the equation of the line in

Writing the equations of lines, however, requires the use of other forms depending on the given properties of the function:

1. THE SLOPE- INTERCEPT FORM- the linear function has been defined in terms of the equation f(x) = mx +b. this form is called the slope intercept form.

2. THE POINT- SLOPE FORM- IF the graph of linear function y has a slope m and passes through the point ( x₁ , y₁) , then its equation is y - y₁= m (x - x₁).

3. THE TWO –POINT FORM – if the graph of the linear function y passes through the point ( x₁, y₁) and (x₂, y₂), its equation according to the point – slope form is y - y₁ = m (x - x₁). But by its definition m = (y₂-y₁ )/(x₂-x₁). By substitution y - y1 = (y2-y1 )/(x2-x1) (x - x1).

Read the details about slope and an example of slope in

Given: Find the equation of the line of the form y = mx + b that passes through the following pairs of points. 9. (-15/2 , 1/3) and (- 1/2, 1/3)

STEPS:

Substitute the values to the TWO- POINT FORM, then transform the resulting equation in the required form: SimplifySOLUTION:

X₁ = -15/2, x₂ = -1/2,

Y₁ = 1/3, y₂=1/3

y - y₁ = ((y₂-y₁)/(x₂-x₁)) (x - x₁)

y- 1/3 = (1/3-1/3)/(-1/2-( -15/2)) ( x - (- 15/2))

y - 1/3 = ((0/ 7))( x+15/2)

y -1/3 = 0 (x +15/2)

y -1/3 = 0 + 0

y= 1/3

the equation is y= 1/3

Read the details about an example of slope and write the equation of the line in

Writing the equations of lines, however, requires the use of other forms depending on the given properties of the function:

1. THE SLOPE- INTERCEPT FORM- the linear function has been defined in terms of the equation f(x) = mx +b. this form is called the slope intercept form.

2. THE POINT- SLOPE FORM- IF the graph of linear function y has a slope m and passes through the point ( x1 , y1) , then its equation is y - y1 = m (x - x1).

3. THE TWO –POINT FORM – if the graph of the linear function y passes through the point ( x1, y1) and (x2, y2), its equation according to the point – slope form is y - y1 = m (x - x1). But by its definition m = (y2-y1 )/(x2-x1). By substitution y - y1 = (y2-y1 )/(x2-x1) (x - x1).

Read the details about slope and an example of slope in

Given: Find the equation of the line of the form y = mx + b that passes through the following pairs of points. 6. (0, 1/2) and (1, -1/2 )

STEPS:

Substitute the values to the TWO- POINT FORM, then transform the resulting equation in the required form:

Simplify

SOLUTION;

X1 = 0, x2 = 1,

Y1 = 1/2, y2 = -1/2

y - y1 = (y2-y1 )/(x2-x1) (x - x1)

y- 1/2 = (-1/2-1/2)/(0- 1) ( x -0)

y -1/2 = ((-1)/-1 ))( x-0)

y -1/2 = 1 ( x-0)

y-1/2 = x -0

y = x + 1/2

the equation is y = x + 1/2

Read the details about an example of slope and write the equation of the line in

2. THE POINT- SLOPE FORM- IF the graph of linear function y has a slope m and passes through the point ( x₁ , y₁) , then its equation is y - y₁ = m (x - x₁).

3. THE TWO –POINT FORM – if the graph of the linear function y passes through the point ( x₁ y₁) and (x₂, y₂), its equation according to the point – slope form is y - y₁= m (x - x₁). But by its definition m = (y₂-y₁)/(x2-x₁). By substitution y - y₁ = (y₂-y₁)/(x₂-x₁) (x - x₁).

Read the details about slope and an example of slope in

Given: Find the equation of the line of the form y = mx + b that passes through the following pairs of points. 8. (-1/2, -5/2) and (- 3/2, 3/2)

STEPS:

Substitute the values to the TWO- POINT FORM, then transform the resulting equation in the required form: SimplifySOLUTION;X₁ = -1/2, X₂ = -3/2,

Y₁= -5/2, y₂ =3/2

y - y₁ = (y₂-y₁)/(x₂-x₁) (x - x₁)

y- -5/2 = (3/2 - ( -5/2))/(-3/2- (-1/2)) ( x -( -1/2))

y +5/2 = ((4/ -1)( x+1/2)

y + 5/2 = -4(x +1/2)

y + 5/2 = -4x -2

y= -4x -2 -5/2

y = -4x -9/2

the equation is y = -4x -9/2

Read the details about an example of slope and write the equation of the line in

THE TWO –POINT FORM – if the graph of the linear function y passes through the point ( x₁, y₁) and (x₂, y₂), its equation according to the point – slope form is y - y₁= m (x - x₁). But by its definition m = (y₂-y₁ )/(x₂-x₁)

By substitution y - y1 = (y₂-y₁ )/(x₂-x₁) (x - x₁).

Read the details about slope and an example of slope in

Given: Find the equation of the line of the form y = mx + b that passes through the following pairs of points. 7. (7/2, 1) and (- 1/2, 2)

STEPS:

Substitute the values to the TWO- POINT FORM, then transform the resulting equation in the required form: SimplifySOLUTION;X1 = 7/2, x2 = -1/2,

Y1 = 1, y2 = 2

y - y1 = (y2-y1 )/(x2-x1) (x - x1)

y- 1 = (2-1)/(-1/2- 7/2) ( x -7/2)

y -1 = (1/-4 )( x-7/2)

y -1 = -1/4x +7/8

y = -1/4x + 7/8 +1

y = -1/4x + 15/6

the equation is y = -1/4x +15/6

Read the details about an example of slope and write the equation of the line in

2. THE POINT- SLOPE FORM- IF the graph of linear function y has a slope m and passes through the point ( x₁ , y₁) , then its equation is y - y₁= m (x - x₁).

3. THE TWO –POINT FORM – if the graph of the linear function y passes through the point ( x₁ y₁) and (x₂, y₂), its equation according to the point – slope form is y - y₁ = m (x - x₁). But by its definition m = (y₂-y₁ )/(x₂-x₁)

By substitution y - y₁= (y₂-y1 )/(x₂-x1) (x - x₁).

Read the details about slope and an example of slope in

Given: Find the equation of the line of the form y = mx + b that passes through the following pairs of points. 3. (3, -1) and (7, -5)

STEPS:

Substitute the values to the TWO- POINT FORM, then transform the resulting equation in the required form: SimplifySOLUTION;

X₁ = 3, x₂ = 7,

Y₁ = -1, y₂= -5

y - y₁ = ((y₂-y₁)/(x₂-x₁))(x - x₁)

y- (-1) = ((-5--1)/(7-3) )( x -3)

y + 1 =( (-5 +1)/4) ( x-3)

y +1 = -4/4 ( x-3)

y+1 = -1 ( x-3)

y+1= -x +3

y = -x +3 -1

y= -x +2

the equation is y= -x +2Read the details about an example of slope and write the equation of the line in

2. THE POINT- SLOPE FORM- IF the graph of linear function y has a slope m and passes through the point ( x₁ , y₁) , then its equation is y - y₁ = m (x - x₁).

3. THE TWO –POINT FORM – if the graph of the linear function y passes through the point ( x₁ y₁) and (x₂, y₂), its equation according to the point – slope form is y - y₁ = m (x - x₁). But by its definition m = (y₂-y₁)/(x₂-x₁)

By substitution y - y₁ = (y₂-y₁ )/(x₂-x₁) (x - x₁).

Read the details about slope and an example of slope in

Given: Find the equation of the line of the form y = mx + b that passes through the following pairs of points. 4. (-8, 5) and (-9, 11)

STEPS: Substitute the values to the TWO- POINT FORM, then transform the resulting equation in the required form: SimplifySOLUTION;X1 = -8, x2 = -9,

Y1 = 5, y2 = 11

y - y1 = (y₂-y₁ )/(x₂-x₁) (x - x₁)

y- 5 = (11-5)/(-9- -8) ( x - -8)

y -5 = ((6)/-9 +8 ))( x+8)

y -5 = ((6/ -1)) ( x+8)

y-5 = -6 ( x+8)

y -5 = -6x -48

y = -6x -48 +5

y= -6x -43

the equation is y= -6x -43

Read the details about an example of slope and write the equation of the line in

2. THE POINT- SLOPE FORM- IF the graph of linear function y has a slope m and passes through the point ( x1 , y1) , then its equation is y - y1 = m (x - x1).

3. THE TWO –POINT FORM – if the graph of the linear function y passes through the point ( x₁, y₁ and (x₂, y₂), its equation according to the point – slope form is y - y₁ = m (x - x₁). But by its definition m = (y₂-y₁ )/(x₂-x₁)

By substitution y - y₁ = (y₂-y₁ )/(x₂-x₁)( (x - x1)).

Read the details about slope and an example of slope in

Given: Find the equation of the line of the form y = mx + b that passes through the following pairs of points. 1. (3, 4) and (4, 7)

STEPS: Substitute the values to the TWO- POINT FORM, then transform the resulting equation in the required form: simplifySOLUTION;X1 = 3, x2 = 4,

Y1 = 4, y2 = 7

y - y₁ = (y₂-y₁ )/(x₂-x₁)( (x - x₁))

y- 4 = (7-4)/(4-3) ( x -3)

y-4 = 3/1 ( x-3)

y -4 = 3x -9

y= 3x -9 +4

y = 3x -5

the equation is y = 3x -5

Read the details about an example of slope and write the equation of the line in

2. THE POINT- SLOPE FORM- IF the graph of linear function y has a slope m and passes through the point ( x₁ , y₁) , then its equation is y - y₁= m (x - x₁).

3. THE TWO –POINT FORM – if the graph of the linear function y passes through the point ( x₁, y₁) and (x₂, y₂), its equation according to the point – slope form is y - y₁ = m (x - x1). But by its definition m = (y₂-y₁ )/(x₂-x₁). By substitution y - y₁ = (y₂-y₁ )/(x₂-x₁) (x - x₁).

Read the details about slope and an example of slope in

Given: Find the equation of the line of the form y = mx + b that passes through the following pairs of points. 5. (-1, 10) and (0, 15)

STEPS:

1. Substitute the values to the TWO- POINT FORM, then transform the resulting equation in the required form:

2. Simplify

SOLUTION;

X₁ = -1, x₂= 0,

Y₁= 10, y₂= 15

y - y₁ =( (y₂-y₁ )/(x₂-x₁)) (x - x₁)

y- 10 = ((15-10)/(0- -1)) ( x - -1)

y -10 = ((5/1 ))( x+1)

y -10 = (5) ( x+1)

y-10 = 5x +5

y = 5x +5 +10

y = 5x +15

the equation is y = 5x +15

Read the details about an example of slope and write the equation of the line in