Question

suppose that the given line has a slope of -2/3 and a y-intercept of (0,5/3). which of the following points is also a solution to the line? select all apply
A. (5,5/3)
B. (1,1)
C. (4,-1)
D. (-3,7)
E. (0,0)

Answer 1

Answer:

From five given points it is find that points (1 , 1) and (4 , -1) will apply

Step-by-step explanation:

According to question,

Slop of line (m) = $\frac{-2}{3}$

And y-intercept is ( 0, $\frac{5}{3}$)

So from above slope and points, the equation of line can be written as

y = mx + c

i.e $\frac{5}{3}$ = $\frac{-2}{3}$ x + c

    $\frac{5}{3}$ = $\frac{-2}{3}$ (0) + c

    $\frac{5}{3}$ = 0 + c

Or, c = $\frac{5}{3}$

A) With points ( 5, $\frac{5}{3}$ )

   At x = 5, y =$\frac{-2}{3}$ (5) + $\frac{5}{3}$

            or, y = $\frac{-10}{3}$ + $\frac{5}{3}$

            so, y = $\frac{-5}{3}$

Hence this points do not apply

B) With points ( 1 , 1 )

   At x = 1, y =  $\frac{-2}{3}$ (1) +  $\frac{5}{3}$

      or,      y =  $\frac{-2+5}{3}$

      So,     y =  $\frac{3}{3}$

                y = 1

Hence this points will apply

C) With points ( 4 , -1 )

    At x = 4 , y =  $\frac{-2}{3}$ (4) +  $\frac{5}{3}$

                    y =  $\frac{-8+5}{3}$

                    y =  $\frac{-3}{3}$

             So,  y= -1

Hence this points will apply

D) With points (-3 ,7)

    At x = - 3, y = $\frac{-2}{3}$ (-3) +  $\frac{5}{3}$

                     y = $\frac{14}{3}$

 Hence this point will not apply

E) with points (0 , 0)

    At x 0,     y =  $\frac{-2}{3}$ (0) +  $\frac{5}{3}$

               Or, y = 0 +  $\frac{5}{3}$

                     y =  $\frac{5}{3}$

Hence this point will not apply

∴ From above five given points it is find that points (1 , 1) and (4 , -1) apply

Answer