Question

1. Write the standard form of the line that passes through the given points. Include your work in your final answer.

(3, 1) and (-2, 3)
2. (4, 7) and (0, 7)
3. (2, 3) and (2, 5)
4.Write the slope-intercept form of the line with a slope of 2 and a y -intercept of -4. Include your work in your final answer.
5. Write the standard form of the line that is parallel to 2 x + 3 y = 4 and passes through the point (1, -4). Include your work in your final answer.
6. Write the standard form of the line that contains a slope of 2/3 and passes through the point (1, 1). Include your work in your final answer.

Answer 1

Part 1)
`2x+5y=11`

Part 2)
`y=7`

Part 3)
`x=2`

Part 4)
`y=2x-4`

Part 5)
`2x+3y=-10`

Part 6)
`2x-3y=-1`

Explanation:

Part 1) Write the standard form of the line that passes through the given points

(3, 1) and (-2, 3)

we know that

The equation of the line in standard form is equal to

Ax+By=C

where

A is a positive integer

B and C are integers

step 1

Find the slope m

`m=(3-1)/(-2-3)`

`m=-2/5`

step 2

Find the equation in point slope form

`y-y1=m(x-x1)`

we have

`m=-2/5` and point
`(3,1)`

substitute

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

`y=-(2/5)x+(6/5)+1`

`y=-(2/5)x+(11/5)`

Convert to standard form

Multiply by 5 both sides

`5y=-2x+11`

`2x+5y=11` -----> equation in standard form

Part 2) Write the standard form of the line that passes through the given points

(4, 7) and (0, 7)

we know that

The equation of the line in standard form is equal to

Ax+By=C

where

A is a positive integer

B and C are integers

step 1

Find the slope m

`m=(7-7)/(0-4)=0`

This is a horizontal line (parallel to the x-axis)

The equation of the line is

`y=7`

Part 3) Write the standard form of the line that passes through the given points

(2, 3) and (2, 5)

we know that

The equation of the line in standard form is equal to

Ax+By=C

where

A is a positive integer

B and C are integers

step 1

Find the slope m

`m=(5-3)/(2-2)`

`m=2/0` ----> the slope is undefined

This is a vertical line (parallel to the y-axis)

The equation of the line is

`x=2`

Part 4) Write the slope-intercept form of the line with a slope of 2 and a y -intercept of -4.

we know that

The equation of the line into slope-intercept form is equal to

`y=mx+b`

where

m is the slope and b is the y-intercept

we have

`m=2`

`b=-4`

substitute

`y=2x-4`

Part 5) Write the standard form of the line that is parallel to 2 x + 3 y = 4 and passes through the point (1, -4).

we know that

If two lines are parallel, then their slopes are the same

we have

`2x+3y=4`

isolate the variable y

`3y=4-2x`

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

The slope of the given line is

`m=-2/3`

so

Find the equation of the line with slope m=-2/3 and passes through the point (1,-4)

`y-y1=m(x-x1)`

substitute

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

`y=-(2/3)x+(2/3)-4`

`y=-(2/3)x-(10/3)`

Convert to standard form

Multiply by 3 both sides

`3y=-2x-10`

`2x+3y=-10`

Part 6) Write the standard form of the line that contains a slope of 2/3 and passes through the point (1, 1)

Find the equation in point slope form

`y-y1=m(x-x1)`

we have

`m=2/3` and point
`(1,1)`

substitute

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

`y=(2/3)x-(2/3)+1`

`y=(2/3)x+(1/3)`

Multiply by 3 both sides

`3y=2x+1`

`2x-3y=-1`