Question

Here is the graph of a linear equation. H. The equation of the line is y=5/4x + 1/4

Answer 1

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)

`m=(y_2-y_1)/(x_2-x_1)=(2-1)/(3-(-1))=(1)/(4)`

So the slope of the line is m= 1/4. Let's find out the point were the line cross the y axis:

`\begin{gathered} 1=(1)/(4)(-1)+b \\ 1+(1)/(4)=b \\ b=(5)/(4) \end{gathered}`

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