Answer:
[tex]y=3x[/tex]
[tex]b=2a+1[/tex]
[tex]t=3r+3[/tex]
Step-by-step explanation:
Assuming you wish to create a linear equation for each set of ordered pairs...
First calculate the slope by using the slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
where m is the slope and [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are two ordered pairs of the set.
Then use the point-slope form of the linear equation:
[tex]y-y_1=m(x-x_1)[/tex]
Question a
[tex](x_1,y_1)=(2,6)[/tex]
[tex](x_2,y_2)=(3,9)[/tex]
[tex]\implies m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{9-6}{3-2}=3[/tex]
[tex]\implies y-6=3(x-2)[/tex]
[tex]\implies y=3x[/tex]
Question b
[tex](a_1,b_1)=(2,5)[/tex]
[tex](a_2,b_2)=(3,7)[/tex]
[tex]\implies m=\dfrac{b_2-b_1}{a_2-a_1}=\dfrac{7-5}{3-2}=2[/tex]
[tex]\implies b-5=2(a-2)[/tex]
[tex]\implies b=2a+1[/tex]
Question c
[tex](r_1,t_1)=(1,6)[/tex]
[tex](r_2,t_2)=(2,9)[/tex]
[tex]\implies m=\dfrac{t_2-t_1}{r_2-r_1}=\dfrac{9-6}{2-1}=3[/tex]
[tex]\implies t-6=3(r-1)[/tex]
[tex]\implies t=3r+3[/tex]
