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Using the given equation find the missing coordinates of the points and then find the slope of the line for each equation:

1) 7x−5y=12
A (......; 9), B (4;........)
The slope is ..............

2) y=−3/7x+3
A(...; 6), B(9; ...)
The slope is ..........

3) y=0.3x+1
A(...; 9), B(5; ...)
The slope is ..........

4) 6.3x+9y=2
A(...; 1/3), B(2/3; ...)
The slope is ..........

5) y−5x=8
A(...; 7), B(8; ...)
The slope is ..........

Respuesta :

calculista

Answer:

Part 1) [tex]A(57/7,9),B(4,16/5), m=7/5[/tex]

Part 2) [tex]A(-7,6),B(9,-6/7), m=-3/7[/tex]  

Part 3) [tex]A(80/3,9),B(5,2.5), m=0.3[/tex]  

Part 4)  [tex]A(-10/63,1/3),B(2/3,-22/90), m=-0.7[/tex]

Part 5)  [tex]A(-1/5,7),B(8,48), m=5[/tex]

Step-by-step explanation:

we know that

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

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-coordinate of the y-intercept

Part 1) we have

[tex]7x-5y=12[/tex]

step 1

Find the slope  

[tex]7x-5y=12[/tex]

isolate the variable y

[tex]y=(7/5)x-(12/5)[/tex]

so

the slope is [tex]m=(7/5)[/tex]

step 2

Find the missing coordinate of point A

To find the x-coordinate of point A substitute the value of y-coordinate in the equation

[tex]9=(7/5)x-(12/5)[/tex]

[tex](7/5)x=9+(12/5)[/tex]

[tex](7/5)x=(57/5)[/tex]

[tex]x=(57/7)[/tex]

step 3

Find the missing coordinate of point B

To find the y-coordinate of point B substitute the value of x-coordinate in the equation

[tex]y=(7/5)(4)-(12/5)[/tex]

[tex]y=(28/5)-(12/5)[/tex]

[tex]y=(16/5)[/tex]  

Part 2) we have

[tex]y=-(3/7)x+3[/tex]

step 1

Find the slope  

the slope is [tex]m=-(3/7)[/tex]

step 2

Find the missing coordinate of point A

To find the x-coordinate of point A substitute the value of y-coordinate in the equation

[tex]6=-(3/7)x+3[/tex]

[tex](3/7)x=3-6[/tex]

[tex](3/7)x=-3[/tex]

[tex]x=-7[/tex]

step 3

Find the missing coordinate of point B

To find the y-coordinate of point B substitute the value of x-coordinate in the equation

[tex]y=-(3/7)(9)+3[/tex]  

[tex]y=-(27/7)+3[/tex]  

[tex]y=-(6/7)[/tex]  

Part 3) we have

[tex]y=0.3x+1[/tex]

step 1

Find the slope  

the slope is [tex]m=0.3[/tex]

step 2

Find the missing coordinate of point A

To find the x-coordinate of point A substitute the value of y-coordinate in the equation

[tex]9=0.3x+1[/tex]

[tex]0.3x=9-1[/tex]

[tex]0.3x=8[/tex]

[tex]x=80/3[/tex]

step 3

Find the missing coordinate of point B

To find the y-coordinate of point B substitute the value of x-coordinate in the equation

[tex]y=0.3(5)+1[/tex]

[tex]y=2.5[/tex]

Part 4) we have

[tex]6.3x+9y=2[/tex]

step 1

Find the slope  

[tex]6.3x+9y=2[/tex]

isolate the variable y

[tex]y=-(0.7)x+(2/9)[/tex]

so

the slope is [tex]m=-0.7[/tex]

step 2

Find the missing coordinate of point A

To find the x-coordinate of point A substitute the value of y-coordinate in the equation

[tex](1/3)=-(0.7)x+(2/9)[/tex]

 [tex](0.7)x=(2/9)-(1/3)[/tex]

 [tex](0.7)x=(2/9)-(1/3)[/tex]

 [tex](0.7)x=-(1/9)[/tex]  

 [tex]x=-(10/63)[/tex]  

step 3

Find the missing coordinate of point B

To find the y-coordinate of point B substitute the value of x-coordinate in the equation

[tex]y=-(0.7)(2/3)+(2/9)[/tex]

[tex]y=-(14/30)+(2/9)[/tex]

[tex]y=-(22/90)[/tex]  

Part 5) we have

[tex]y-5x=8[/tex]

step 1

Find the slope  

[tex]y-5x=8[/tex]  ------->  [tex]y=5x+8[/tex]

the slope is [tex]m=5[/tex]

step 2

Find the missing coordinate of point A

To find the x-coordinate of point A substitute the value of y-coordinate in the equation

[tex]7=5x+8[/tex]

[tex]5x=7-8[/tex]

[tex]x=-1/5[/tex]

step 3

Find the missing coordinate of point B

To find the y-coordinate of point B substitute the value of x-coordinate in the equation

[tex]y=5(8)+8[/tex]

[tex]y=48[/tex]

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