plot the point on this function with a y - value of 9. what is the x - value of this point?

Explanation:

Step1: Determine the linear function equation

Observe the y-intercept is 2 (when ( x = 0 ), ( y = 2 )). Calculate the slope using two points, e.g., ( (0, 2) ) and ( (2, 3) ):
( \text{slope} = \frac{3 - 2}{2 - 0} = \frac{1}{2} ).
Equation: ( y = \frac{1}{2}x + 2 ).

Step2: Solve for ( x ) when ( y = 9 )

Substitute ( y = 9 ) into the equation:
( 9 = \frac{1}{2}x + 2 ).
Subtract 2 from both sides: ( 7 = \frac{1}{2}x ).
Multiply both sides by 2: ( x = 14 ).

Answer:

14