Given: A line goes through points (0,2) and (1,1). Equation of the line formed between these two points will be:
[tex]\begin{gathered} \frac{y-2}{x-0}=\frac{2-1}{0-1} \\ \frac{y-2}{x}=-2 \\ y-2=-2x \\ 2x+y=2 \end{gathered}[/tex]Thus, the eqaution of the line formed through points (0,2) and (1,1) is 2x+y=2.
Now solve equations 2x+y=2 and y=3x+3 to find the x coordinate of the intersection of this line.
[tex]\begin{gathered} y=3x+3---(1) \\ 2x+y=2---(2) \end{gathered}[/tex]Substitute equation (1) in equation (2).
[tex]\begin{gathered} 2x+3x+3=2 \\ 5x+3=2 \\ 5x=-1 \\ x=-\frac{1}{5} \end{gathered}[/tex]Thus, the x coordinate of the intersection of this line is x=-1/5.
