Question

Find the equation of the line through (5/4,-1) and has equal intercepts. Write your answer in general form.

Answer 1

The equation of a line with a slope, m, and y-intercept, c is given in slope-intercept form as:

`y=mx+c`

To find the x-intercept, substitute y=0 into the equation:

`\begin{gathered} 0=mx+c \\ \Rightarrow mx=-c \\ \Rightarrow(mx)/(m)=-(c)/(m) \\ \Rightarrow x=-(c)/(m) \end{gathered}`

Since it is given that the line has equal intercepts, equate the y-intercept to the x-intercept:

`\begin{gathered} c=-(c)/(m) \\ \text{Cross Multiply:} \\ \Rightarrow cm=-c \\ \Rightarrow(cm)/(c)=-(c)/(c) \\ \Rightarrow m=-1 \end{gathered}`

It follows that the slope of the line is -1.

Recall that the equation of a line through (a,b), with slope, m in point-slope form is given as:

`y-b=m(x-a)`

Substitute (a,b)=(5/4,-1) and m=-1 into the equation:

`\begin{gathered} y-(-1)=-1(x-(5)/(4)) \\ \Rightarrow y+1=-x+(5)/(4) \\ \Rightarrow x+y=(5)/(4)-1 \\ \Rightarrow x+y=(1)/(4) \end{gathered}`

The equation in general form Ax+Bx=C is:

x+y=1/4.