Hello!
First, let's make a graph with these points:
As we can see, it is a function in the form ax + b = 0 (1st degree).
To solve this exercise, we can calculate the slope and then write the equation of the line in the slope-intercept form.
So, let's calculate the slope:
[tex]Slope=\frac{y_B-y_A}{x_A-x_B}=\frac{0-(-2)}{1-0}=\frac{+2}{1}=2[/tex]Now, let's write it in the slope-intercept form as y = mx + b:
• m, is the slope
,• b ,is the y-intercept
,• x ,and ,y ,are generic coordinates
To solve it, let's replace x and y with the coordinates of point C (third):
[tex]\begin{gathered} y=mx+b \\ y=2\cdot x+b \\ -4=2\cdot(-1)+b \\ -4=-2+b \\ -4+2=b \\ b=-2 \end{gathered}[/tex]Now, we know all unknows, let's rewrite it:
[tex]\begin{gathered} y=mx+b \\ y=2x-2 \end{gathered}[/tex]Oops! But we don't have this option, right?
So, we must remember one thing: when we are talking about functions, f(x) and y mean the same.
So, we just have to replace y with f(x) and the answer will be:
[tex]f(x)=2x-2[/tex]
