Question

6 A line goes through Paints (0,2) and (1,1). what is the x-coordinate of the intersection of this line with the line y=3x+3?

Answer 1

Given: A line goes through points (0,2) and (1,1). Equation of the line formed between these two points will be:

`\begin{gathered} (y-2)/(x-0)=(2-1)/(0-1) \\ (y-2)/(x)=-2 \\ y-2=-2x \\ 2x+y=2 \end{gathered}`

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.

`\begin{gathered} y=3x+3---(1) \\ 2x+y=2---(2) \end{gathered}`

Substitute equation (1) in equation (2).

`\begin{gathered} 2x+3x+3=2 \\ 5x+3=2 \\ 5x=-1 \\ x=-(1)/(5) \end{gathered}`

Thus, the x coordinate of the intersection of this line is x=-1/5.