Question

Find the equation of the line that contains the point whose coordinates are (5, -1) and has a slope 1/5

Answer 1

The slope-point form of the equation of a line with slope m that passes through the point (x_0,y_0), is:

`y=m(x-x_0)+y_0`

To find the equation of the line that contains the point with coordinates (5,-1) and has a slope 1/5, susbtitute x_0=5, y_0=-1 and m=1/5:

`y=(1)/(5)(x-5)-1`

The equation can be simplified to be written in slope-intercept form:

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

Therefore, the equation of such a line (in slope-intercept form) is:

`y=(1)/(5)x-2`