Question

Draw a line that is parallel to a line on the graph and passes through the point (-1,0)

Answer 1

First, calculate the slope of the line in the image using the formula below

`\begin{gathered} (x_1,y_1),(x_2,y_2) \\ \Rightarrow slope=(y_2-y_1)/(x_2-x_1) \end{gathered}`

Therefore, in our case,

`\begin{gathered} (2,0),(0,-5) \\ \Rightarrow slope=m=(-5-0)/(0-2)=(5)/(2) \end{gathered}`

On the other hand, two parallel lines must have the same slope; thus, the slope of the line we need to draw is the same as that of the line in the image.

Thus, the equation of the line we need to draw is

`\begin{gathered} m=(5)/(2),(-1,0) \\ \Rightarrow y=(5)/(2)(x+1) \\ \Rightarrow y=(5)/(2)x+(5)/(2) \end{gathered}`

We are given the point (-1,0), to find another point on the line set a value of x different than -1 in the equation above; for example, after setting x=1,

`\begin{gathered} x=1 \\ \Rightarrow y=(5)/(2)*1+(5)/(2)=(10)/(2)=5 \\ \Rightarrow(1,5) \end{gathered}`

Draw the point (1,5) on the plane; then, draw a line that crosses (-1,0) and (1,5), as shown in the image below (the red line)