Question

Can you pleas answer the question b and c or even one of them

Answer 1

#a

• (3,9)
• (10,30)

`\\ \rm\Rrightarrow m=(30-9)/(10-3)=21/7=3`

#b

• (2,5)
• (5,11)

`\\ \rm\Rrightarrow m=(11-5)/(5-2)=6/3=2`

#c

• (1,6)
• (5,18)

`\\ \rm\Rrightarrow m=(18-6)/(5-1)=3`

• m is slope

Answer 2

`y=3x`

`b=2a+1`

`t=3r+3`

Explanation:

Assuming you wish to create a linear equation for each set of ordered pairs...

First calculate the slope by using the slope formula:

`m=(y_2-y_1)/(x_2-x_1)`

where m is the slope and
`(x_1,y_1)` and
`(x_2,y_2)` are two ordered pairs of the set.

Then use the point-slope form of the linear equation:

`y-y_1=m(x-x_1)`

Question a

`(x_1,y_1)=(2,6)`

`(x_2,y_2)=(3,9)`

`\implies m=(y_2-y_1)/(x_2-x_1)=(9-6)/(3-2)=3`

`\implies y-6=3(x-2)`

`\implies y=3x`

Question b

`(a_1,b_1)=(2,5)`

`(a_2,b_2)=(3,7)`

`\implies m=(b_2-b_1)/(a_2-a_1)=(7-5)/(3-2)=2`

`\implies b-5=2(a-2)`

`\implies b=2a+1`

Question c

`(r_1,t_1)=(1,6)`

`(r_2,t_2)=(2,9)`

`\implies m=(t_2-t_1)/(r_2-r_1)=(9-6)/(2-1)=3`

`\implies t-6=3(r-1)`

`\implies t=3r+3`