Respuesta :
The equation of a line with a slope, m, and y-intercept, c is given in slope-intercept form as:
[tex]y=mx+c[/tex]To find the x-intercept, substitute y=0 into the equation:
[tex]\begin{gathered} 0=mx+c \\ \Rightarrow mx=-c \\ \Rightarrow\frac{mx}{m}=-\frac{c}{m} \\ \Rightarrow x=-\frac{c}{m} \end{gathered}[/tex]Since it is given that the line has equal intercepts, equate the y-intercept to the x-intercept:
[tex]\begin{gathered} c=-\frac{c}{m} \\ \text{Cross Multiply:} \\ \Rightarrow cm=-c \\ \Rightarrow\frac{cm}{c}=-\frac{c}{c} \\ \Rightarrow m=-1 \end{gathered}[/tex]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:
[tex]y-b=m(x-a)[/tex]Substitute (a,b)=(5/4,-1) and m=-1 into the equation:
[tex]\begin{gathered} y-(-1)=-1(x-\frac{5}{4}) \\ \Rightarrow y+1=-x+\frac{5}{4} \\ \Rightarrow x+y=\frac{5}{4}-1 \\ \Rightarrow x+y=\frac{1}{4} \end{gathered}[/tex]The equation in general form Ax+Bx=C is:
x+y=1/4.
