A linear function is written in the following form: y= mx +b
Let's find out which function is it, by choosing two points. In this case, (-1,1) and (3,2)
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-1}{3-(-1)}=\frac{1}{4}[/tex]
So the slope of the line is m= 1/4. Let's find out the point were the line cross the y axis:
[tex]\begin{gathered} 1=\frac{1}{4}(-1)+b \\ 1+\frac{1}{4}=b \\ b=\frac{5}{4} \end{gathered}[/tex]
So the function is f(x) = 1/4x +5/4 let's examine our options now
A) yes, One solution is the point (3,2): True, this point belong to the line
C) One solution of the equation is (-1,1): True this point belong to the line
D) One solution of the equation is (1, 3/2) True, 1/4 (1)+5/4= 6/4 = 3/2
E) There are two solutions. True, since He didn't say only then it is true
F) There are infinitely many solutions. True, there are more than 2, 3 points for that line and since the line is infinite.
G) True, as it was demonstrated above.
H) False, The function is f(x) = 1/4x +5/4 and not the y=5/4x + 1/4
