53.7k views
4 votes
Find the equation of the line through (5/4,-1) and has equal intercepts. Write your answer in general form.

1 Answer

3 votes

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.

User Salmane
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories