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:

$y=\frac{1}{5}(x-5)-1$

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

$\begin{gathered} \Rightarrow y=\frac{1}{5}x-\frac{1}{5}\times5-1 \\ =\frac{1}{5}x-1-1 \\ =\frac{1}{5}x-2 \end{gathered}$

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

$y=\frac{1}{5}x-2$