Answer:
(0, 2) and (2, 5) are solutions to the function.
Step-by-step explanation:
Given the following linear function:
[tex]\displaystyle\mathsf{f(x)\:=\:\frac{3}{2}x\:+\:2 }[/tex]
"f(x)" is a function notation.
"f" represents the function name. In function notations, you can use any letter to represent a function name. However, "f" is commonly used to express function notations.
"x" is your input variable. This is the x-values that you substitute into the function to get an output, or y-value.
f(x) is your output value.
We are also given the following points: (0, 2) and (2, 5).
In order to determine whether these points work with the given function, simply substitute their values into the function.
(0, 2) where x = 0, y = 2:
[tex]\displaystyle\mathsf{f(x)\:=\:\frac{3}{2}x\:+\:2 }[/tex]
[tex]\displaystyle\mathsf{f(0)\:=\:\frac{3}{2}(0)\:+\:2 }[/tex] ⇒ The function notation, "f(0)" simply means the function of zero, which corresponds to the input value of zero (0).
Next, substitute the value of y = 2 into the function as an output value:
[tex]\displaystyle\mathsf{2\:=\:\frac{3}{2}(0)\:+\:2 }[/tex]
2 = 0 + 2
2 = 2 (True statement). This means that the point, (0, 2), is a solution to the given function. The point (0, 2) represent the given function's y-intercept, which is the point on the graph where it crosses the y-axis. The y-coordinate of 2 is the value of b in the slope-intercept form, y = mx + b.
(2, 5) where x = 2, y = 5:
We will do the same process for (2, 5):
[tex]\displaystyle\mathsf{f(x)\:=\:\frac{3}{2}x\:+\:2 }[/tex]
[tex]\displaystyle\mathsf{f(2)\:=\:\frac{3}{2}(2)\:+\:2 }[/tex]
Substitute the value of y = 5 into the function as an output value:
[tex]\displaystyle\mathsf{5\:=\:\frac{3}{2}(2)\:+\:2 }[/tex]
5 = 3 + 2
5 = 5 (True statement). This means that the point, (2, 5), is also a solution to the given function.
