Answer: The answers is (A) [tex]m=-2,~~c=2.[/tex] and (B) [tex]m=-\dfrac{1}{2},~~c=1.[/tex]
Step-by-step explanation: We are to select the slope and y-intercept of the linear function that is graphed to the left.
We know that the equation of a straight line in slope-intercept form is given by
[tex]y=mx+c,[/tex]
where 'm' is the slope and 'c' is the y-intercept of the line.
Also, a straight line with a positive slope (m>0) rises from left to right whereas a line with a negative slope (m < 0) falls from right to left.
Option (A) is
[tex]m=-2,~~c=2.[/tex]
Since 'm' is negative, so the function is graphed to the left.
Option (B) is
[tex]m=-\dfrac{1}{2},~~c=1.[/tex]
Since 'm' is negative, so the function is graphed to the left.
Option (C) is
[tex]m=\dfrac{1}{2},~~c=2.[/tex]
Since 'm' is positive, so the function is graphed to the right.
Option (D) is
[tex]m=2,~~c=1.[/tex]
Since 'm' is positive, so the function is graphed to the right.
Thus, (A) and (B) are the correct options.
